Finite Group Databasebeta

← #16922425

Subgroups — #16922425

Order 4352.

514 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 155 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#14528764C212yesmaximal
2#14526607C214yesmaximal, complemented
3C17×#2296C211yesmaximal, characteristic
4C2×C4⋊#3622—22no—
5C2×C22⋊#3622—22no—
6#11762564C2214yes—
7C2×C17×#117C411yescharacteristic
8C2×C17×#117C411yescharacteristic
9C22×C42×C17C2211yescharacteristic
10C17×#389C412yes—
11C17×#389C2212yes—
12C17×#385—22no—
13C4×C4⋊C4×C17—22no—
14C23×C4×C17C2×C411yescharacteristic
15C23×C4×C17D412yes—
16C17×#117—22no—
17C17×#117—42no—
18C17×#117C814yescomplemented
19C2×C4⋊C4×C17—22no—
20C2×C4⋊C4×C17—22no—
21C2×C4⋊C4×C17C2×C412yes—
22C2×C4⋊C4×C17C2×C412yes—
23C2×C22⋊C4×C17—21no—
24C2×C22⋊C4×C17—21no—
25C2×C42×C17—21no—
26C2×C42×C17—21no—
27C2×C42×C17—42no—
28C2×C42×C17C2×C411yescharacteristic
29C2×C42×C17D412yes—
30C2×C42×C17C2311yescharacteristic
31C22×#3622—24no—
32C17×#95—22no—
33C17×#95—22no—
34C22⋊#3622—44no—
35C4⋊#3622—44no—
36C24×C17C22⋊C411yescharacteristic
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—22no—
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17—42no—
44C22×C4×C17—42no—
45C22×C4×C17C22⋊C412yes—
46C22×C4×C17C22⋊C411yescharacteristic
47C22×C4×C17C2×C812yes—
48C22×C4×C17M1612yes—
49C22×C4×C17C22×C411yescharacteristic
50C22×C4×C17C2×D412yes—
51C4⋊C4×C17—22no—
52C4⋊C4×C17—42no—
53C4⋊C4×C17—44no—
54C4⋊C4×C17—42no—
55C4⋊C4×C17—42no—
56C4⋊C4×C17C2×C814yes—
57C22⋊C4×C17—24no—
58C22⋊C4×C17—42no—
59C42×C17—24no—
60C42×C17—24no—
61C42×C17—41no—
62C42×C17—41no—
63C42×C17—42no—
64C2×#3622—44no—
65C2×#3622—44no—
66C2×#3622—44no—
67#7598—171nomaximal, Sylow
68C23×C17—21no—
69C23×C17—21no—
70C23×C17—22no—
71C23×C17—22no—
72C23×C17C22⋊C812yes—
73C23×C17C2×C22⋊C411yescharacteristic
74C2×C4×C17—22no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—22no—
78C2×C4×C17—24no—
79C2×C4×C17—24no—
80C2×C4×C17—24no—
81C2×C4×C17—22no—
82C2×C4×C17—22no—
83C2×C4×C17—22no—
84C2×C4×C17—44no—
85C2×C4×C17—44no—
86C2×C4×C17—42no—
87C2×C4×C17—42no—
88C2×C4×C17—42no—
89C2×C4×C17—42no—
90C2×C4×C17—42no—
91C2×C4×C17C22⋊C812yes—
92C2×C4×C17#9912yes—
93C2×C4×C17#10112yes—
94C2×C4×C17C22×C811yescharacteristic
95C2×C4×C17C2×M1611yescharacteristic
96C2×C4×C17AGL(1,ℤ/8)12yes—
97C2×C4×C17#13712yes—
98#3622—84no—
99#2296D1711yescharacteristic
100#1797—172no—
101#1271—174no—
102C22×C17—22no—
103C22×C17—24no—
104C22×C17—41no—
105C22×C17—41no—
106C22×C17—42no—
107C22×C17C2×C22⋊C811yescharacteristic
108C22×C17C2×#9911yescharacteristic
109C22×C17C2×#10111yescharacteristic
110C22×C17#41712yes—
111C22×C17#42112yes—
112C4×C17—21no—
113C4×C17—21no—
114C4×C17—22no—
115C4×C17—22no—
116C4×C17—44no—
117C4×C17—42no—
118C4×C17—82no—
119C4×C17#32414yes—
120C2×#117Dic1711yescharacteristic
121C2×#117Dic1711yescharacteristic
122C22×C42C2×D1711yescharacteristic
123C2×C4⋊C8—342no—
124C2×C22⋊C8—342no—
125#389Dic1712yes—
126#389C2×D1712yes—
127#385—22no—
128C4×C4⋊C4—22no—
129#336—174no—
130C2×C17—42no—
131C2×C17C2×#32411yescharacteristic
132C2×C17#147712yes—
133C2×C17#151312yes—
134C2×C17#153711yescharacteristic
135C2×C17#156111yescharacteristic
136C23×C4C2×Dic1711yescharacteristic
137C23×C4C22⋊D1712yes—
138C22×C8—344no—
139#117—22no—
140#117—42no—
141#117#362214yescomplemented
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4C2×Dic1712yes—
145C2×C4⋊C4C2×Dic1712yes—
146C2×C22⋊C4—21no—
147C2×C22⋊C4—21no—
148C2×C42—21no—
149C2×C42—21no—
150C2×C42—42no—
151C2×C42C2×Dic1711yescharacteristic
152C2×C42C22⋊D1712yes—
153C2×C42C22×D1711yescharacteristic
154C4⋊C8—684no—
155C22⋊C8—684no—
156#95—22no—
157#95—22no—
158C17#759811yescharacteristic, complemented, Sylow
159C24C22⋊Dic1711yescharacteristic
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4C2×#362212yes—
169C22×C4#6322312yes—
170C22×C4C22⋊Dic1712yes—
171C22×C4C22⋊Dic1711yescharacteristic
172C22×C4C22×Dic1711yescharacteristic
173C22×C4C2×C22⋊D1712yes—
174C2×C8—684no—
175C2×C8—684no—
176C2×C8—684no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—44no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4C2×#362214yes—
183C22⋊C4—24no—
184C22⋊C4—42no—
185C42—24no—
186C42—24no—
187C42—41no—
188C42—41no—
189C42—42no—
190C23—21no—
191C23—21no—
192C23—22no—
193C23—22no—
194C23C22⋊#362212yes—
195C23C2×C22⋊Dic1711yescharacteristic
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—44no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4C22⋊#362212yes—
214C2×C4#1058750512yes—
215C2×C4#1058750712yes—
216C2×C4C22×#362211yescharacteristic
217C2×C4C2×#6322311yescharacteristic
218C2×C4#1058763512yes—
219C2×C4#1058763712yes—
220C8—1364no—
221C22—22no—
222C22—24no—
223C22—41no—
224C22—42no—
225C22—41no—
226C22C2×C22⋊#362211yescharacteristic
227C22C2×#1058750511yescharacteristic
228C22C2×#1058750711yescharacteristic
229C22#1176281012yes—
230C22#1176282612yes—
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—42no—
236C4—44no—
237C4—82no—
238C4#1176253514yes—
239C2—42no—
240C2C2×#1176253511yescharacteristic
241C2#1452717112yes—
242C2#1452732712yes—
243C2#1452742211yescharacteristic
244C2#1452752211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic17
commutatorC2×C4×C17C22×C8
FrattiniC2×C42C22×D17
FittingC17×#2296C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2296D17
hypocenterC17#7598
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. #14526607C2semidirect
18. C17×#117C8semidirect
141. #117#3622semidirect
158. C17#7598semidirect

Maximal subgroups

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

subgroupindex
#145287642
#145266072
C17×#22962
#759817