Finite Group Databasebeta

← #16946899

Subgroups — #16946899

Order 4352.

372 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 59 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#14534026C211yesmaximal, characteristic, complemented
2#14527821C212yesmaximal
3#14526810C212yesmaximal, complemented
4#14526730C211yesmaximal, characteristic, complemented
5C17×#2039C211yesmaximal, characteristic
6#11763125—22no—
7#11762748—21no—
8#11762748C2212yes—
9#11762708—22no—
10#11762674—22no—
11C4×C4⋊Dic17—21no—
12#11762543—22no—
13#11762535C2212yes—
14C17×#537C2211yescharacteristic
15C2×C17×#104—21no—
16C17×#417—21no—
17C17×#384C2211yescharacteristic
18C17×#343C2211yescharacteristic
19C2×#41×C17—21no—
20C2×M16×C17—21no—
21C17×C22⋊Q8—41no—
22C17×#121—22no—
23C17×#121—41no—
24C2×C4⋊C4×C17—22no—
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C4⋊C4×C17C2311yescharacteristic
27C2×C42×C17D411yescharacteristic
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17D412yes—
32C2×C4×Dic17—22no—
33C17×#104—42no—
34C17×#103—41no—
35C17×#102—41no—
36#10587503—42no—
37#10587502—22no—
38#10587502—21no—
39#10587502—22no—
40#10587502—22no—
41#10587502D412yes—
42C22⋊#3622—22no—
43#10587479—42no—
44#41×C17—41no—
45#41×C17—41no—
46#41×C17—41no—
47#41×C17—41no—
48C2×Q8×C17—21no—
49C2×D4×C17—21no—
50C2×D4×C17—22no—
51C2×D4×C17—41no—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—41no—
55C22×C4×C17C2×D412yes—
56C22×C4×C17C2×D411yescharacteristic
57C22×Dic17—22no—
58C22×Dic17—22no—
59M16×C17—41no—
60M16×C17—41no—
61C2×C8×C17—41no—
62C4⋊C4×C17—22no—
63C4⋊C4×C17—41no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—44no—
66C22⋊C4×C17—42no—
67C42×C17—21no—
68C42×C17SD1612yes—
69C4⋊Dic17—42no—
70C4⋊Dic17—42no—
71C4⋊Dic17—42no—
72C4⋊Dic17—81no—
73C4×Dic17—44no—
74C2×#3622—42no—
75#12181—171nomaximal, Sylow
76C23×C17—41no—
77C23×C17#12011yescharacteristic
78Q8×C17—41no—
79Q8×C17—41no—
80D4×C17—41no—
81D4×C17—41no—
82D4×C17—82no—
83D4×C17—81no—
84D4×C17—81no—
85C2×C4×C17—22no—
86C2×C4×C17—22no—
87C2×C4×C17—22no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—22no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—81no—
96C2×C4×C17—81no—
97C2×C4×C17C2×SD1611yescharacteristic
98C2×C4×C17#13711yescharacteristic
99C2×Dic17—42no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103C2×Dic17—42no—
104C2×Dic17—42no—
105C8×C17—81no—
106#3622—82no—
107#2571—171no—
108#2039D1711yescharacteristic
109#1616—172no—
110#1353—172no—
111#1325—171no—
112C22×C17—21no—
113C22×C17—21no—
114C22×C17—81no—
115C22×C17—81no—
116C22×C17—81no—
117C22×C17#44811yescharacteristic
118C22×C17#45411yescharacteristic
119C22×C17B(4,𝔽2)11yescharacteristic
120C4×C17—24no—
121C4×C17—21no—
122C4×C17—21no—
123C4×C17—42no—
124C4×C17—81no—
125C4×C17—81no—
126Dic17—82no—
127Dic17—82no—
128#537C2×D1711yescharacteristic
129#481—342no—
130C2×#104—21no—
131#417—21no—
132#400—172no—
133#400—341no—
134#389—342no—
135#384C2×D1711yescharacteristic
136#382—342no—
137C4×C4⋊C4—341no—
138#343C2×D1711yescharacteristic
139#327—342no—
140#324—172no—
141C2×C17—21no—
142C2×C17—21no—
143C2×C17—161no—
144C2×C17#159911yescharacteristic
145C2×C17#219811yescharacteristic
146C2×C17#220411yescharacteristic
147C2×#41—21no—
148C2×M16—21no—
149C22⋊Q8—41no—
150#121—22no—
151#121—41no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—172no—
154C2×C4⋊C4—341no—
155C2×C4⋊C4—341no—
156C2×C4⋊C4—341no—
157C2×C4⋊C4C22⋊D1711yescharacteristic
158C2×C4⋊C4C22×D1711yescharacteristic
159C2×C42—342no—
160C2×C42C22⋊D1711yescharacteristic
161#106—682no—
162#104—42no—
163#103—41no—
164#102—41no—
165#102—682no—
166C22⋊C8—342no—
167#95—172no—
168#95—341no—
169#95—342no—
170#95—342no—
171#95—342no—
172C17#1218111yescharacteristic, complemented, Sylow
173#41—41no—
174#41—41no—
175#41—41no—
176#41—41no—
177C2×Q8—21no—
178C2×D4—21no—
179C2×D4—22no—
180C2×D4—41no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—41no—
184C22×C4—342no—
185C22×C4—342no—
186C22×C4D4×D1712yes—
187C22×C4C2×C22⋊D1711yescharacteristic
188M16—41no—
189M16—41no—
190C2×C8—41no—
191C2×C8—682no—
192C4⋊C4—22no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—44no—
196C4⋊C4—682no—
197C4⋊C4—682no—
198C4⋊C4—682no—
199C4⋊C4—1361no—
200C22⋊C4—42no—
201C42—21no—
202C42—684no—
203C42#6322912yes—
204C23—41no—
205C23#1058762311yescharacteristic
206Q8—41no—
207Q8—41no—
208D4—41no—
209D4—41no—
210D4—82no—
211D4—81no—
212D4—81no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—682no—
226C2×C4—682no—
227C2×C4—682no—
228C2×C4—682no—
229C2×C4—682no—
230C2×C4—682no—
231C2×C4C2×#6322911yescharacteristic
232C2×C4#1058763711yescharacteristic
233C8—81no—
234C8—1362no—
235C22—21no—
236C22—21no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22#1176294711yescharacteristic
241C22#1176298111yescharacteristic
242C22#1176299511yescharacteristic
243C4—24no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—81no—
248C4—81no—
249C4—1362no—
250C4—1362no—
251C2—21no—
252C2—21no—
253C2—161no—
254C2#1452772311yescharacteristic
255C2#1453077911yescharacteristic
256C2#1453080911yescharacteristic
subgroupG/H
centerC22#11762995
commutator, cosocleC2×C4⋊C4×C17C23
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2039C2
socleC22×C17B(4,𝔽2)
prime radicalC17×#537C22
hypercenter#2039D17
hypocenterC17#12181
LCSG ▷ C2×C4⋊C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #14534026C2semidirect
3. #14526810C2semidirect
4. #14526730C2semidirect
172. C17#12181semidirect

Maximal subgroups

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

subgroupindex
#145340262
#145278212
#145268102
#145267302
C17×#20392
#1218117