Finite Group Databasebeta

← C2×C17×#2911 #16917849

Subgroups — C2×C17×#2911 #16917849

Order 4352.

2878 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C17C211yesmaximal, characteristic
2C22×C17×#117C212yesmaximal
3C17×#2911C2116yesmaximal, direct product factor
4C2×C17×#428C218yesmaximal, complemented
5C2×C17×#427C214yesmaximal, complemented
6C24×C4×C17C2211yescharacteristic
7C22×M16×C17C4116yescomplemented
8C22×M16×C17C2214yes—
9C22×M16×C17C2218yes—
10C23×C8×C17C2212yes—
11C2×C17×#117—22no—
12C2×C17×#117—28no—
13C2×C17×#117—22no—
14C2×C17×#117C2214yes—
15C2×C17×#117C2214yes—
16C2×C17×#117C22116yes—
17C22×C4⋊C4×C17C2214yes—
18C22×C22⋊C4×C17—22no—
19C22×C42×C17—22no—
20C17×#428C22164yescomplemented
21C17×#427C22132yescomplemented
22C2×C17×#107C2218yescomplemented
23C2×C17×#106C2218yescomplemented
24C25×C17D411yescharacteristic
25C23×C4×C17—24no—
26C23×C4×C17C2×C418yes—
27C23×C4×C17D411yescharacteristic
28C23×C4×C17D414yes—
29C23×C4×C17D412yes—
30C23×C4×C17Q818yes—
31C23×C4×C17C2312yes—
32C23×C4×C17C2314yes—
33C23×C4×C17C2311yescharacteristic
34C2×M16×C17C2×C4132yescomplemented
35C2×M16×C17C2×C4164yescomplemented
36C2×M16×C17C23116yes—
37C22×C8×C17C2×C4116yescomplemented
38C22×C8×C17C2314yes—
39C22×C8×C17C2318yes—
40C17×#117—216no—
41C17×#117—28no—
42C17×#117—28no—
43C17×#117—216no—
44C17×#117C23116yes—
45C17×#117C23116yes—
46C2×C4⋊C4×C17—24no—
47C2×C4⋊C4×C17—28no—
48C2×C4⋊C4×C17C2318yes—
49C2×C4⋊C4×C17C23116yes—
50C2×C22⋊C4×C17—24no—
51C2×C22⋊C4×C17—24no—
52C2×C22⋊C4×C17—216no—
53C2×C42×C17—24no—
54C2×C42×C17—216no—
55C2×C42×C17—24no—
56C17×#107C23132yescomplemented
57C17×#106C23132yescomplemented
58C24×C17—44no—
59C24×C17C4⋊C418yes—
60C24×C17C2×D412yes—
61C24×C17C2×D411yescharacteristic
62C24×C17C2×D414yes—
63C22×C4×C17—216no—
64C22×C4×C17—28no—
65C22×C4×C17—416no—
66C22×C4×C17C4⋊C418yes—
67C22×C4×C17C4⋊C4132yes—
68C22×C4×C17C4⋊C4116yes—
69C22×C4×C17C22×C414yes—
70C22×C4×C17C22×C418yes—
71C22×C4×C17C22×C4116yes—
72C22×C4×C17C2×D412yes—
73C22×C4×C17C2×D418yes—
74C22×C4×C17C2×D414yes—
75C22×C4×C17C2×D412yes—
76C22×C4×C17C2×D414yes—
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×Q818yes—
79C22×C4×C17C2×Q8116yes—
80C22×C4×C17C2×Q814yes—
81C22×C4×C17C2411yescharacteristic
82C22×C4×C17C2412yes—
83C22×C4×C17C2414yes—
84M16×C17C22×C4164yescomplemented
85C2×C8×C17C22×C4116yes—
86C2×C8×C17C22×C4132yescomplemented
87C2×C8×C17C2418yes—
88C4⋊C4×C17—216no—
89C4⋊C4×C17—28no—
90C4⋊C4×C17C24116yes—
91C22⋊C4×C17—216no—
92C22⋊C4×C17—216no—
93C42×C17—216no—
94C42×C17—216no—
95C2×#2911C1711yesmaximal, characteristic, direct product factor, Sylow
96C23×C17—28no—
97C23×C17—24no—
98C23×C17—416no—
99C23×C17—48no—
100C23×C17C2×C4⋊C414yes—
101C23×C17C2×C4⋊C418yes—
102C23×C17C2×C4⋊C4116yes—
103C23×C17C22×D412yes—
104C23×C17C22×D414yes—
105C23×C17C22×D411yescharacteristic
106C2×C4×C17—216no—
107C2×C4×C17—432no—
108C2×C4×C17—416no—
109C2×C4×C17C2×C4⋊C418yes—
110C2×C4×C17C2×C4⋊C4132yes—
111C2×C4×C17C2×C4⋊C4116yes—
112C2×C4×C17C2×C4⋊C4116yes—
113C2×C4×C17C2×C4⋊C418yes—
114C2×C4×C17C2×C4⋊C414yes—
115C2×C4×C17C23×C412yes—
116C2×C4×C17C23×C414yes—
117C2×C4×C17C23×C418yes—
118C2×C4×C17C22×D412yes—
119C2×C4×C17C22×D414yes—
120C2×C4×C17C22×D411yescharacteristic
121C2×C4×C17C22×Q814yes—
122C2×C4×C17C22×Q818yes—
123C2×C4×C17C22×Q812yes—
124C2×C4×C17C2511yescharacteristic
125C8×C17C23×C4116yes—
126C23×M16C2×C1711yescharacteristic
127C22×#117C2×C1712yes—
128#2911C2×C17116yesdirect product factor
129C2×#428C2×C1718yescomplemented
130C2×#427C2×C1714yescomplemented
131C22×C17—216no—
132C22×C17—28no—
133C22×C17—28no—
134C22×C17—24no—
135C22×C17—416no—
136C22×C17C22×C4⋊C414yes—
137C22×C17C22×C4⋊C418yes—
138C22×C17C22×C4⋊C412yes—
139C22×C17#57514yes—
140C22×C17C23×D411yescharacteristic
141C4×C17—416no—
142C4×C17C22×C4⋊C412yes—
143C4×C17C22×C4⋊C418yes—
144C4×C17C22×C4⋊C414yes—
145C4×C17C24×C411yescharacteristic
146C4×C17C23×Q811yescharacteristic
147C24×C4C22×C1711yescharacteristic
148C22×M16C4×C17116yescomplemented
149C22×M16C22×C1714yes—
150C22×M16C22×C1718yes—
151C23×C8C22×C1712yes—
152C2×#117—22no—
153C2×#117—28no—
154C2×#117—22no—
155C2×#117C22×C1714yes—
156C2×#117C22×C1714yes—
157C2×#117C22×C17116yes—
158C22×C4⋊C4C22×C1714yes—
159C22×C22⋊C4—22no—
160C22×C42—22no—
161#428C22×C17164yescomplemented
162#427C22×C17132yescomplemented
163C2×#107C22×C1718yescomplemented
164C2×#106C22×C1718yescomplemented
165C2×C17—28no—
166C2×C17—24no—
167C2×C17#291114yesdirect product factor
168C2×C17C23×C4⋊C411yescharacteristic
169C2×C17C2×#57512yes—
170C25D4×C1711yescharacteristic
171C23×C4—24no—
172C23×C4C2×C4×C1718yes—
173C23×C4D4×C1711yescharacteristic
174C23×C4D4×C1714yes—
175C23×C4D4×C1712yes—
176C23×C4Q8×C1718yes—
177C23×C4C23×C1712yes—
178C23×C4C23×C1711yescharacteristic
179C23×C4C23×C1714yes—
180C2×M16C2×C4×C17132yescomplemented
181C2×M16C2×C4×C17164yescomplemented
182C2×M16C23×C17116yes—
183C22×C8C2×C4×C17116yescomplemented
184C22×C8C23×C1714yes—
185C22×C8C23×C1718yes—
186#117—216no—
187#117—28no—
188#117—28no—
189#117—216no—
190#117C23×C17116yes—
191#117C23×C17116yes—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—28no—
194C2×C4⋊C4C23×C1718yes—
195C2×C4⋊C4C23×C17116yes—
196C2×C22⋊C4—24no—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—216no—
199C2×C42—24no—
200C2×C42—216no—
201C2×C42—24no—
202#107C23×C17132yescomplemented
203#106C23×C17132yescomplemented
204C17C2×#291111yescharacteristic, direct product factor, Sylow
205C24—44no—
206C24C4⋊C4×C1718yes—
207C24C2×D4×C1711yescharacteristic
208C24C2×D4×C1712yes—
209C24C2×D4×C1714yes—
210C22×C4—216no—
211C22×C4—28no—
212C22×C4—416no—
213C22×C4C4⋊C4×C1718yes—
214C22×C4C4⋊C4×C17116yes—
215C22×C4C4⋊C4×C17132yes—
216C22×C4C22×C4×C1714yes—
217C22×C4C22×C4×C1718yes—
218C22×C4C22×C4×C17116yes—
219C22×C4C2×D4×C1712yes—
220C22×C4C2×D4×C1718yes—
221C22×C4C2×D4×C1714yes—
222C22×C4C2×D4×C1712yes—
223C22×C4C2×D4×C1714yes—
224C22×C4C2×D4×C1711yescharacteristic
225C22×C4C2×Q8×C1718yes—
226C22×C4C2×Q8×C1714yes—
227C22×C4C2×Q8×C17116yes—
228C22×C4C24×C1711yescharacteristic
229C22×C4C24×C1714yes—
230C22×C4C24×C1712yes—
231M16C22×C4×C17164yescomplemented
232C2×C8C22×C4×C17116yes—
233C2×C8C22×C4×C17132yescomplemented
234C2×C8C24×C1718yes—
235C4⋊C4—216no—
236C4⋊C4—28no—
237C4⋊C4C24×C17116yes—
238C22⋊C4—216no—
239C22⋊C4—216no—
240C42—216no—
241C42—216no—
242C23—28no—
243C23—24no—
244C23—416no—
245C23—48no—
246C23C2×C4⋊C4×C1714yes—
247C23C2×C4⋊C4×C1718yes—
248C23C2×C4⋊C4×C17116yes—
249C23C22×D4×C1712yes—
250C23C22×D4×C1714yes—
251C23C22×D4×C1711yescharacteristic
252C2×C4—216no—
253C2×C4—432no—
254C2×C4—416no—
255C2×C4C2×C4⋊C4×C1718yes—
256C2×C4C2×C4⋊C4×C17132yes—
257C2×C4C2×C4⋊C4×C17116yes—
258C2×C4C2×C4⋊C4×C17116yes—
259C2×C4C2×C4⋊C4×C1714yes—
260C2×C4C2×C4⋊C4×C1718yes—
261C2×C4C23×C4×C1712yes—
262C2×C4C23×C4×C1714yes—
263C2×C4C23×C4×C1718yes—
264C2×C4C22×D4×C1712yes—
265C2×C4C22×D4×C1714yes—
266C2×C4C22×D4×C1711yescharacteristic
267C2×C4C22×Q8×C1718yes—
268C2×C4C22×Q8×C1714yes—
269C2×C4C22×Q8×C1712yes—
270C2×C4C25×C1711yescharacteristic
271C8C23×C4×C17116yes—
272C22—28no—
273C22—24no—
274C22—216no—
275C22—28no—
276C22—416no—
277C22C22×C4⋊C4×C1714yes—
278C22C22×C4⋊C4×C1718yes—
279C22C22×C4⋊C4×C1712yes—
280C22C17×#57514yes—
281C22C23×D4×C1711yescharacteristic
282C4—416no—
283C4C22×C4⋊C4×C1712yes—
284C4C22×C4⋊C4×C1714yes—
285C4C22×C4⋊C4×C1718yes—
286C4C24×C4×C1711yescharacteristic
287C4C23×Q8×C1711yescharacteristic
288C2—28no—
289C2—24no—
290C2C17×#291114yesdirect product factor
291C2C23×C4⋊C4×C1711yescharacteristic
292C2C2×C17×#57512yes—
subgroupG/H
centerC22×C4×C17C2×D4
commutatorC4C24×C4×C17
Frattini, cosocleC2×C4C25×C17
socleC23×C17C22×D4
prime radicalC25×C17D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C17 ◁ C24×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
3. C17×#2911C2direct (N × H)
4. C2×C17×#428C2semidirect
5. C2×C17×#427C2semidirect
7. C22×M16×C17C4semidirect
20. C17×#428C22semidirect
21. C17×#427C22semidirect
22. C2×C17×#107C22semidirect
23. C2×C17×#106C22semidirect
34. C2×M16×C17C2×C4semidirect
35. C2×M16×C17C2×C4semidirect
37. C22×C8×C17C2×C4semidirect
56. C17×#107C23semidirect
57. C17×#106C23semidirect
84. M16×C17C22×C4semidirect
86. C2×C8×C17C22×C4semidirect
95. C2×#2911C17direct (N × H)
128. #2911C2×C17direct (N × H)
129. C2×#428C2×C17semidirect
130. C2×#427C2×C17semidirect
148. C22×M16C4×C17semidirect
161. #428C22×C17semidirect
162. #427C22×C17semidirect
163. C2×#107C22×C17semidirect
164. C2×#106C22×C17semidirect
167. C2×C17#2911direct (N × H)
180. C2×M16C2×C4×C17semidirect
181. C2×M16C2×C4×C17semidirect
183. C22×C8C2×C4×C17semidirect
202. #107C23×C17semidirect
203. #106C23×C17semidirect
204. C17C2×#2911direct (N × H)
231. M16C22×C4×C17semidirect
233. C2×C8C22×C4×C17semidirect
290. C2C17×#2911direct (N × H)

Maximal subgroups

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

subgroupindex
C23×M16×C172
C22×C17×#1172
C17×#29112
C2×C17×#4282
C2×C17×#4272
C2×#291117