Finite Group Databasebeta

← C17×#11503 #16869247

Subgroups — C17×#11503 #16869247

Order 4352.

670 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C17×#2309C211yesmaximal, characteristic
2C17×#1464C212yesmaximal, complemented
3C17×#1316C214yesmaximal, complemented
4C23×D4×C17C411yescharacteristic
5C2×C17×#117C411yescharacteristic
6C2×C17×#117C2211yescharacteristic
7C17×#432—22no—
8C17×#390—22no—
9C17×#390—22no—
10C17×#379C412yes—
11C17×#379C2212yes—
12C17×#324—22no—
13C17×#323C2214yes—
14C25×C17C2×C412yes—
15C22×D4×C17—24no—
16C22×D4×C17—21no—
17C22×D4×C17—21no—
18C22×D4×C17—41no—
19C22×D4×C17—41no—
20C22×D4×C17—42no—
21C23×C4×C17C2×C411yescharacteristic
22C17×#117—41no—
23C17×#117—41no—
24C17×#117—42no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17D412yes—
27C2×C22⋊C4×C17—24no—
28C2×C22⋊C4×C17—24no—
29C2×C22⋊C4×C17C2×C412yes—
30C2×C22⋊C4×C17C2×C411yescharacteristic
31C2×C22⋊C4×C17C2311yescharacteristic
32C2×C42×C17—21no—
33C2×C42×C17D412yes—
34C17×C4⋊C8—42no—
35C17×C22⋊C8—24no—
36C17×#97—42no—
37C24×C17—22no—
38C24×C17—22no—
39C24×C17—42no—
40C24×C17—42no—
41C24×C17—84no—
42C24×C17M1614yes—
43C24×C17C22×C411yescharacteristic
44C2×D4×C17—24no—
45C2×D4×C17—24no—
46C2×D4×C17—48no—
47C2×D4×C17—48no—
48C2×D4×C17—42no—
49C2×D4×C17—42no—
50C2×D4×C17—41no—
51C2×D4×C17—41no—
52C2×D4×C17—42no—
53C22×C4×C17—22no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—22no—
57C22×C4×C17—22no—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C412yes—
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C2×D412yes—
62C2×C8×C17—44no—
63C4⋊C4×C17—42no—
64C4⋊C4×C17—42no—
65C22⋊C4×C17—41no—
66C22⋊C4×C17—41no—
67C22⋊C4×C17—42no—
68C22⋊C4×C17—84no—
69C22⋊C4×C17—84no—
70C42×C17—22no—
71C42×C17—22no—
72C42×C17—42no—
73#11503C1711yesmaximal, characteristic, direct product factor, Sylow
74C23×C17—21no—
75C23×C17—21no—
76C23×C17—24no—
77C23×C17—42no—
78C23×C17—44no—
79C23×C17—44no—
80C23×C17—44no—
81C23×C17—44no—
82C23×C17—42no—
83C23×C17—42no—
84C23×C17—84no—
85C23×C17—84no—
86C23×C17—88no—
87C23×C17—88no—
88C23×C17C2×C22⋊C411yescharacteristic
89C23×C17C2×M1612yes—
90D4×C17—44no—
91D4×C17—44no—
92D4×C17—48no—
93C2×C4×C17—24no—
94C2×C4×C17—24no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—22no—
100C2×C4×C17—22no—
101C2×C4×C17—42no—
102C2×C4×C17—42no—
103C2×C4×C17—44no—
104C2×C4×C17—42no—
105C2×C4×C17#9911yescharacteristic
106C2×C4×C17#9911yescharacteristic
107C2×C4×C17#10012yes—
108C8×C17—84no—
109#2309C2×C1711yescharacteristic
110#1464C2×C1712yescomplemented
111#1316C2×C1714yescomplemented
112C22×C17—22no—
113C22×C17—22no—
114C22×C17—42no—
115C22×C17—42no—
116C22×C17—44no—
117C22×C17—44no—
118C22×C17—42no—
119C22×C17—44no—
120C22×C17—84no—
121C22×C17—88no—
122C22×C17—88no—
123C22×C17—84no—
124C22×C17#40711yescharacteristic
125C22×C17C2×#9911yescharacteristic
126C22×C17C2×#10011yescharacteristic
127C4×C17—21no—
128C4×C17—21no—
129C4×C17—22no—
130C4×C17—42no—
131C4×C17—42no—
132C4×C17—82no—
133C23×D4C4×C1711yescharacteristic
134C2×#117C4×C1711yescharacteristic
135C2×#117C22×C1711yescharacteristic
136#432—22no—
137#390—22no—
138#390—22no—
139#379C4×C1712yes—
140#379C22×C1712yes—
141#324—22no—
142#323C22×C1714yes—
143C2×C17—21no—
144C2×C17—21no—
145C2×C17—42no—
146C2×C17—84no—
147C2×C17#146211yescharacteristic
148C2×C17#212212yes—
149C25C2×C4×C1712yes—
150C22×D4—24no—
151C22×D4—21no—
152C22×D4—21no—
153C22×D4—41no—
154C22×D4—41no—
155C22×D4—42no—
156C23×C4C2×C4×C1711yescharacteristic
157#117—41no—
158#117—41no—
159#117—42no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4D4×C1712yes—
162C2×C22⋊C4—24no—
163C2×C22⋊C4—24no—
164C2×C22⋊C4C2×C4×C1712yes—
165C2×C22⋊C4C2×C4×C1711yescharacteristic
166C2×C22⋊C4C23×C1711yescharacteristic
167C2×C42—21no—
168C2×C42D4×C1712yes—
169C4⋊C8—42no—
170C22⋊C8—24no—
171#97—42no—
172C17#1150311yescharacteristic, direct product factor, Sylow
173C24—22no—
174C24—22no—
175C24—42no—
176C24—42no—
177C24—84no—
178C24M16×C1714yes—
179C24C22×C4×C1711yescharacteristic
180C2×D4—24no—
181C2×D4—24no—
182C2×D4—48no—
183C2×D4—48no—
184C2×D4—42no—
185C2×D4—42no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4—42no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4C22⋊C4×C1711yescharacteristic
195C22×C4C22⋊C4×C1711yescharacteristic
196C22×C4C22⋊C4×C1712yes—
197C22×C4C2×D4×C1712yes—
198C2×C8—44no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C22⋊C4—41no—
202C22⋊C4—41no—
203C22⋊C4—42no—
204C22⋊C4—84no—
205C22⋊C4—84no—
206C42—22no—
207C42—22no—
208C42—42no—
209C23—21no—
210C23—21no—
211C23—24no—
212C23—42no—
213C23—44no—
214C23—44no—
215C23—44no—
216C23—44no—
217C23—42no—
218C23—42no—
219C23—84no—
220C23—84no—
221C23—88no—
222C23—88no—
223C23C2×C22⋊C4×C1711yescharacteristic
224C23C2×M16×C1712yes—
225D4—44no—
226D4—44no—
227D4—48no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4—42no—
240C2×C4C17×#9911yescharacteristic
241C2×C4C17×#9911yescharacteristic
242C2×C4C17×#10012yes—
243C8—84no—
244C22—22no—
245C22—22no—
246C22—42no—
247C22—42no—
248C22—44no—
249C22—44no—
250C22—42no—
251C22—44no—
252C22—84no—
253C22—88no—
254C22—88no—
255C22—84no—
256C22C17×#40711yescharacteristic
257C22C2×C17×#9911yescharacteristic
258C22C2×C17×#10011yescharacteristic
259C4—21no—
260C4—21no—
261C4—22no—
262C4—42no—
263C4—42no—
264C4—82no—
265C2—21no—
266C2—21no—
267C2—42no—
268C2—84no—
269C2C17×#146211yescharacteristic
270C2C17×#212212yes—
subgroupG/H
center, socleC22×C17C2×#99
commutatorC24C22×C4×C17
Frattini, cosocleC2×C22⋊C4C23×C17
prime radicalC23×D4×C17C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1464C2semidirect
3. C17×#1316C2semidirect
73. #11503C17direct (N × H)
110. #1464C2×C17semidirect
111. #1316C2×C17semidirect
172. C17#11503direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#23092
C17×#14642
C17×#13162
#1150317