Finite Group Databasebeta

← C2×C17×#2983 #16917987

Subgroups — C2×C17×#2983 #16917987

Order 4352.

1978 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C17C211yesmaximal, characteristic
2C17×#2983C2116yesmaximal, direct product factor
3C2×C17×#446C218yesmaximal, complemented
4C2×C17×#432C214yesmaximal
5C2×C17×#431C212yesmaximal
6C23×Q8×C17C411yescharacteristic
7C2×C4×Q8×C17C414yes—
8C2×C4×Q8×C17C418yes—
9C2×C4×Q8×C17C2214yes—
10C2×C4×Q8×C17C2218yes—
11C22×C4⋊C4×C17C412yes—
12C22×C4⋊C4×C17C411yescharacteristic
13C22×C42×C17C2211yescharacteristic
14C22×C42×C17C2212yes—
15C17×#446C22164yescomplemented
16C17×#432C22132yes—
17C17×#431C22116yes—
18C2×C17×C4⋊C8C2214yes—
19C2×C17×C4⋊C8C2218yes—
20C2×C17×C22⋊C8C2214yes—
21C2×C17×#97C2218yes—
22C2×C4×C8×C17C2214yes—
23C22×Q8×C17—28no—
24C22×Q8×C17C2×C414yes—
25C22×Q8×C17C2×C418yes—
26C23×C4×C17C2×C412yes—
27C23×C4×C17C2×C411yescharacteristic
28C23×C4×C17C2×C412yes—
29C23×C4×C17C2×C411yescharacteristic
30C23×C4×C17C2311yescharacteristic
31C22×C8×C17C2318yes—
32C4×Q8×C17C2×C4116yes—
33C4×Q8×C17C2×C4132yes—
34C4×Q8×C17C23116yes—
35C2×C4⋊C4×C17C2×C418yes—
36C2×C4⋊C4×C17C2×C4116yes—
37C2×C4⋊C4×C17C2×C414yes—
38C2×C4⋊C4×C17C2×C418yes—
39C2×C42×C17C2×C414yes—
40C2×C42×C17C2×C418yes—
41C2×C42×C17C2×C412yes—
42C2×C42×C17C2×C414yes—
43C2×C42×C17C2314yes—
44C2×C42×C17C2318yes—
45C2×C42×C17C2312yes—
46C2×C42×C17C2314yes—
47C17×C4⋊C8C23116yes—
48C17×C4⋊C8C23132yes—
49C17×C22⋊C8C23116yes—
50C17×#97C23132yes—
51C4×C8×C17C23116yes—
52C24×C17C22×C411yescharacteristic
53C2×Q8×C17—232no—
54C2×Q8×C17—216no—
55C2×Q8×C17C22×C4116yes—
56C22×C4×C17—28no—
57C22×C4×C17—24no—
58C22×C4×C17—42no—
59C22×C4×C17—44no—
60C22×C4×C17M1618yes—
61C22×C4×C17C22×C418yes—
62C22×C4×C17C22×C414yes—
63C22×C4×C17C22×C412yes—
64C22×C4×C17C22×C414yes—
65C22×C4×C17C22×C411yescharacteristic
66C22×C4×C17C22×C412yes—
67C22×C4×C17C22×C414yes—
68C22×C4×C17C22×C418yes—
69C22×C4×C17C22×C414yes—
70C22×C4×C17C22×C412yes—
71C22×C4×C17C2412yes—
72C22×C4×C17C2411yescharacteristic
73C2×C8×C17—216no—
74C2×C8×C17C24116yes—
75C4⋊C4×C17C22×C4132yes—
76C4⋊C4×C17C22×C4116yes—
77C42×C17C22×C4116yes—
78C42×C17C22×C418yes—
79C42×C17C22×C418yes—
80C42×C17C22×C414yes—
81C42×C17C2414yes—
82C42×C17C2418yes—
83C2×#2983C1711yesmaximal, characteristic, direct product factor, Sylow
84C23×C17—22no—
85C23×C17—22no—
86C23×C17C2×M1614yes—
87C23×C17C23×C412yes—
88C23×C17C23×C411yescharacteristic
89Q8×C17—232no—
90C2×C4×C17—22no—
91C2×C4×C17—216no—
92C2×C4×C17—28no—
93C2×C4×C17—24no—
94C2×C4×C17—28no—
95C2×C4×C17—24no—
96C2×C4×C17—24no—
97C2×C4×C17—44no—
98C2×C4×C17—48no—
99C2×C4×C17C2×M16116yes—
100C2×C4×C17C2×M1618yes—
101C2×C4×C17C23×C412yes—
102C2×C4×C17C23×C414yes—
103C2×C4×C17C23×C418yes—
104C2×C4×C17C23×C418yes—
105C2×C4×C17C23×C411yescharacteristic
106C2×C4×C17C23×C414yes—
107C2×C4×C172−1+414yes—
108C2×C4×C17C2511yescharacteristic
109C8×C17—216no—
110C22×C4×Q8C2×C1711yescharacteristic
111#2983C2×C17116yesdirect product factor
112C2×#446C2×C1718yescomplemented
113C2×#432C2×C1714yes—
114C2×#431C2×C1712yes—
115C22×C17—22no—
116C22×C17—28no—
117C22×C17—22no—
118C22×C17#51912yes—
119C22×C17C22×M1614yes—
120C22×C17C22×M1612yes—
121C22×C17#56812yes—
122C22×C17C24×C411yescharacteristic
123C4×C17—22no—
124C4×C17—28no—
125C4×C17—24no—
126C4×C17—28no—
127C4×C17#51912yes—
128C4×C17C22×M1618yes—
129C4×C17C2×2−1+412yes—
130C23×Q8C4×C1711yescharacteristic
131C2×C4×Q8C4×C1714yes—
132C2×C4×Q8C4×C1718yes—
133C2×C4×Q8C22×C1714yes—
134C2×C4×Q8C22×C1718yes—
135C22×C4⋊C4C4×C1712yes—
136C22×C4⋊C4C4×C1711yescharacteristic
137C22×C42C22×C1711yescharacteristic
138C22×C42C22×C1712yes—
139#446C22×C17164yescomplemented
140#432C22×C17132yes—
141#431C22×C17116yes—
142C2×C4⋊C8C22×C1714yes—
143C2×C4⋊C8C22×C1718yes—
144C2×C22⋊C8C22×C1714yes—
145C2×#97C22×C1718yes—
146C2×C4×C8C22×C1714yes—
147C2×C17—24no—
148C2×C17#298314yesdirect product factor
149C2×C17C2×#51911yescharacteristic
150C2×C17C23×M1611yescharacteristic
151C2×C17C2×#56811yescharacteristic
152C22×Q8—28no—
153C22×Q8C2×C4×C1714yes—
154C22×Q8C2×C4×C1718yes—
155C23×C4C2×C4×C1712yes—
156C23×C4C2×C4×C1711yescharacteristic
157C23×C4C2×C4×C1712yes—
158C23×C4C2×C4×C1711yescharacteristic
159C23×C4C23×C1711yescharacteristic
160C22×C8C23×C1718yes—
161C4×Q8C2×C4×C17116yes—
162C4×Q8C2×C4×C17132yes—
163C4×Q8C23×C17116yes—
164C2×C4⋊C4C2×C4×C1718yes—
165C2×C4⋊C4C2×C4×C1714yes—
166C2×C4⋊C4C2×C4×C17116yes—
167C2×C4⋊C4C2×C4×C1718yes—
168C2×C42C2×C4×C1714yes—
169C2×C42C2×C4×C1712yes—
170C2×C42C2×C4×C1718yes—
171C2×C42C2×C4×C1714yes—
172C2×C42C23×C1712yes—
173C2×C42C23×C1714yes—
174C2×C42C23×C1714yes—
175C2×C42C23×C1718yes—
176C4⋊C8C23×C17116yes—
177C4⋊C8C23×C17132yes—
178C22⋊C8C23×C17116yes—
179#97C23×C17132yes—
180C4×C8C23×C17116yes—
181C17C2×#298311yescharacteristic, direct product factor, Sylow
182C24C22×C4×C1711yescharacteristic
183C2×Q8—232no—
184C2×Q8—216no—
185C2×Q8C22×C4×C17116yes—
186C22×C4—28no—
187C22×C4—24no—
188C22×C4—42no—
189C22×C4—44no—
190C22×C4M16×C1718yes—
191C22×C4C22×C4×C1711yescharacteristic
192C22×C4C22×C4×C1712yes—
193C22×C4C22×C4×C1712yes—
194C22×C4C22×C4×C1714yes—
195C22×C4C22×C4×C1718yes—
196C22×C4C22×C4×C1714yes—
197C22×C4C22×C4×C1714yes—
198C22×C4C22×C4×C1718yes—
199C22×C4C22×C4×C1714yes—
200C22×C4C22×C4×C1712yes—
201C22×C4C24×C1712yes—
202C22×C4C24×C1711yescharacteristic
203C2×C8—216no—
204C2×C8C24×C17116yes—
205C4⋊C4C22×C4×C17132yes—
206C4⋊C4C22×C4×C17116yes—
207C42C22×C4×C17116yes—
208C42C22×C4×C1718yes—
209C42C22×C4×C1718yes—
210C42C22×C4×C1714yes—
211C42C24×C1714yes—
212C42C24×C1718yes—
213C23—22no—
214C23—22no—
215C23C2×M16×C1714yes—
216C23C23×C4×C1712yes—
217C23C23×C4×C1711yescharacteristic
218Q8—232no—
219C2×C4—22no—
220C2×C4—216no—
221C2×C4—28no—
222C2×C4—24no—
223C2×C4—28no—
224C2×C4—24no—
225C2×C4—24no—
226C2×C4—44no—
227C2×C4—48no—
228C2×C4C2×M16×C17116yes—
229C2×C4C2×M16×C1718yes—
230C2×C4C23×C4×C1712yes—
231C2×C4C23×C4×C1714yes—
232C2×C4C23×C4×C1718yes—
233C2×C4C23×C4×C1718yes—
234C2×C4C23×C4×C1711yescharacteristic
235C2×C4C23×C4×C1714yes—
236C2×C4C17×2−1+414yes—
237C2×C4C25×C1711yescharacteristic
238C8—216no—
239C22—28no—
240C22—22no—
241C22—22no—
242C22C17×#51912yes—
243C22C22×M16×C1714yes—
244C22C22×M16×C1712yes—
245C22C17×#56812yes—
246C22C24×C4×C1711yescharacteristic
247C4—28no—
248C4—24no—
249C4—28no—
250C4—22no—
251C4C17×#51912yes—
252C4C22×M16×C1718yes—
253C4C2×C17×2−1+412yes—
254C2—24no—
255C2C17×#298314yesdirect product factor
256C2C2×C17×#51911yescharacteristic
257C2C23×M16×C1711yescharacteristic
258C2C2×C17×#56811yescharacteristic
subgroupG/H
centerC22×C4×C17C24
commutatorC22C24×C4×C17
Frattini, cosocleC2×C4C25×C17
socleC23×C17C23×C4
prime radicalC24×C17C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2983C2direct (N × H)
3. C2×C17×#446C2semidirect
15. C17×#446C22semidirect
83. C2×#2983C17direct (N × H)
111. #2983C2×C17direct (N × H)
112. C2×#446C2×C17semidirect
139. #446C22×C17semidirect
148. C2×C17#2983direct (N × H)
181. C17C2×#2983direct (N × H)
255. C2C17×#2983direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C172
C17×#29832
C2×C17×#4462
C2×C17×#4322
C2×C17×#4312
C2×#298317