Finite Group Databasebeta

← #16923593

Subgroups — #16923593

Order 4352.

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

normal subgroups only

This group has 418 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#14530347C212yesmaximal, complemented
2#14530317C211yesmaximal, characteristic
3#14526607C212yesmaximal, complemented
4#14526605C211yesmaximal, characteristic
5C17×#2724C211yesmaximal, characteristic
6C2×#10587479—21no—
7C2×#10587503—21no—
8#11762679C2211yescharacteristic
9#11762571—22no—
10#11762571—22no—
11#11762564C2211yescharacteristic
12#11762564C2212yes—
13C2×C17×#123—21no—
14C17×#398—21no—
15C17×#397—22no—
16C17×#390C2211yescharacteristic
17C17×#389C2212yes—
18C17×#385—22no—
19C22×D4×C17D411yescharacteristic
20C23×C4×C17—21no—
21C17×#123—42no—
22C17×#123—42no—
23C2×C4⋊C4×C17—22no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17D412yes—
26C2×C4⋊C4×C17D412yes—
27C2×C4⋊C4×C17D411yescharacteristic
28C2×C22⋊C4×C17—22no—
29C2×C22⋊C4×C17—21no—
30C2×C22⋊C4×C17—22no—
31C2×C42×C17C2311yescharacteristic
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—22no—
34C22×#3622—21no—
35C22×#3622—22no—
36C17×#95—22no—
37C17×#95—21no—
38C17×#95—22no—
39#10587503—42no—
40#10587479—42no—
41C24×C17—21no—
42C2×D4×C17—21no—
43C2×D4×C17—41no—
44C2×D4×C17—41no—
45C2×D4×C17SD1612yes—
46C22×C4×C17—22no—
47C22×C4×C17—22no—
48C22×C4×C17—21no—
49C22×C4×C17—42no—
50C22×C4×C17—81no—
51C22×C4×C17—81no—
52C22×C4×C17C2×D411yescharacteristic
53C22×C4×C17C2×D412yes—
54C22×Dic17—41no—
55C4⋊C4×C17—22no—
56C4⋊C4×C17—22no—
57C4⋊C4×C17—41no—
58C4⋊C4×C17—42no—
59C4⋊C4×C17—42no—
60C4⋊C4×C17—42no—
61C4⋊C4×C17—81no—
62C22⋊C4×C17—42no—
63C22⋊C4×C17—44no—
64C22⋊C4×C17—42no—
65C22⋊C4×C17—42no—
66C42×C17—41no—
67C4⋊Dic17—41no—
68C4⋊Dic17—41no—
69C4⋊Dic17—44no—
70C2×#3622—22no—
71C2×#3622—41no—
72C2×#3622—41no—
73C2×#3622—42no—
74C2×#3622—42no—
75C2×#3622—42no—
76#7824—171nomaximal, Sylow
77C23×C17—22no—
78C23×C17—42no—
79C23×C17—41no—
80C23×C17—42no—
81C23×C17—41no—
82C23×C17#12011yescharacteristic
83D4×C17—42no—
84D4×C17—81no—
85C2×C4×C17—21no—
86C2×C4×C17—22no—
87C2×C4×C17—22no—
88C2×C4×C17—21no—
89C2×C4×C17—42no—
90C2×C4×C17—42no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17—41no—
94C2×C4×C17—42no—
95C2×C4×C17—42no—
96C2×C4×C17—42no—
97C2×C4×C17—84no—
98C2×C4×C17C2×SD1611yescharacteristic
99C2×C4×C17#13512yes—
100C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
101C2×C4×C17#13712yes—
102C2×Dic17—81no—
103C2×Dic17—82no—
104#3622—42no—
105#3622—82no—
106#2724D1711yescharacteristic
107#2100—172no—
108#2094—171no—
109#1271—172no—
110#1270—171no—
111C22×C17—42no—
112C22×C17—44no—
113C22×C17—82no—
114C22×C17—81no—
115C22×C17—81no—
116C22×C17#45011yescharacteristic
117C22×C17#45212yes—
118C22×C17#45311yescharacteristic
119C22×C17#45412yes—
120C22×C17#45811yescharacteristic
121C4×C17—21no—
122C4×C17—21no—
123C4×C17—22no—
124C4×C17—22no—
125C4×C17—82no—
126C4×C17—81no—
127C4×C17—82no—
128Dic17—161no—
129C2×#123—21no—
130C2×#106—341no—
131C2×#102—341no—
132#398—21no—
133#397—22no—
134#390C2×D1711yescharacteristic
135#389C2×D1712yes—
136#385—22no—
137#384—171no—
138#340—342no—
139#340—342no—
140#336—171no—
141#336—172no—
142C2×C17—82no—
143C2×C17#161311yescharacteristic
144C2×C17#161512yes—
145C2×C17#163011yescharacteristic
146C2×C17#163512yes—
147C2×C17#165711yescharacteristic
148C22×D4C22⋊D1711yescharacteristic
149C23×C4—21no—
150C22×C8—341no—
151C22×C8—342no—
152#123—42no—
153#123—42no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—342no—
157C2×C4⋊C4—341no—
158C2×C4⋊C4C22⋊D1712yes—
159C2×C4⋊C4C22⋊D1712yes—
160C2×C4⋊C4C22⋊D1711yescharacteristic
161C2×C22⋊C4—22no—
162C2×C22⋊C4—21no—
163C2×C22⋊C4—22no—
164C2×C42C22×D1711yescharacteristic
165#106—682no—
166#102—682no—
167#95—22no—
168#95—21no—
169#95—22no—
170C17#782411yescharacteristic, complemented, Sylow
171C24—21no—
172C2×D4—21no—
173C2×D4—41no—
174C2×D4—41no—
175C2×D4#6322912yes—
176C22×C4—22no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—42no—
180C22×C4—81no—
181C22×C4—81no—
182C22×C4—681no—
183C22×C4C2×C22⋊D1711yescharacteristic
184C22×C4C2×C22⋊D1712yes—
185C2×C8—342no—
186C2×C8—681no—
187C2×C8—681no—
188C2×C8—682no—
189C2×C8—682no—
190C2×C8—682no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—81no—
198C4⋊C4—681no—
199C4⋊C4—681no—
200C4⋊C4—684no—
201C22⋊C4—42no—
202C22⋊C4—44no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C42—41no—
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#1058763911yescharacteristic
212D4—42no—
213D4—81no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—84no—
227C2×C4—1361no—
228C2×C4—1362no—
229C2×C4#1058761811yescharacteristic
230C2×C4C2×#6322911yescharacteristic
231C2×C4#1058763612yes—
232C2×C4#1058763712yes—
233C8—682no—
234C8—1362no—
235C22—42no—
236C22—44no—
237C22—82no—
238C22—81no—
239C22—81no—
240C22#1176296011yescharacteristic
241C22#1176297112yes—
242C22#1176297711yescharacteristic
243C22#1176298212yes—
244C22#1176299911yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—82no—
250C4—81no—
251C4—82no—
252C4—2721no—
253C2—82no—
254C2#1452780411yescharacteristic
255C2#1452781512yes—
256C2#1452790511yescharacteristic
257C2#1452793512yes—
258C2#1452808211yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2724C2
socleC23×C17#120
prime radicalC22×D4×C17D4
hypercenter#2724D17
hypocenterC17#7824
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2724

Complements

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

NH ≅ G/Ntype
1. #14530347C2semidirect
3. #14526607C2semidirect
170. C17#7824semidirect

Maximal subgroups

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

subgroupindex
#145303472
#145303172
#145266072
#145266052
C17×#27242
#782417