Finite Group Databasebeta

← C22×C17×#430 #16917855

Subgroups — C22×C17×#430 #16917855

Order 4352.

2718 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C17C212yesmaximal
2C23×M16×C17C211yesmaximal, characteristic
3C2×C17×#430C2124yesmaximal, direct product factor
4C22×C17×#108C214yesmaximal, complemented
5C24×C4×C17C2211yescharacteristic
6C22×M16×C17—212no—
7C22×M16×C17—22no—
8C22×M16×C17C414yes—
9C22×M16×C17C4112yes—
10C22×M16×C17C2214yes—
11C22×M16×C17C22124yes—
12C22×M16×C17C22112yes—
13C23×C8×C17—22no—
14C23×C8×C17C2212yes—
15C17×#430C22164yesdirect product factor
16C2×C17×#108C22148yescomplemented
17C25×C17Q811yescharacteristic
18C23×C4×C17C2×C412yes—
19C23×C4×C17C2×C416yes—
20C23×C4×C17D416yes—
21C23×C4×C17D412yes—
22C23×C4×C17Q811yescharacteristic
23C23×C4×C17Q816yes—
24C23×C4×C17C2316yes—
25C23×C4×C17C2311yescharacteristic
26C2×M16×C17—224no—
27C2×M16×C17—212no—
28C2×M16×C17—248no—
29C2×M16×C17C2×C4148yes—
30C2×M16×C17C2×C4148yes—
31C2×M16×C17C23124yes—
32C2×M16×C17C23132yes—
33C2×M16×C17C23116yes—
34C22×C8×C17—224no—
35C22×C8×C17—24no—
36C22×C8×C17C2×C414yes—
37C22×C8×C17C2×C4112yes—
38C22×C8×C17C23112yes—
39C17×#108C23164yescomplemented
40C24×C17—44no—
41C24×C17C4⋊C412yes—
42C24×C17C4⋊C416yes—
43C24×C17C2×Q811yescharacteristic
44C24×C17C2×Q816yes—
45C22×C4×C17C4⋊C4112yes—
46C22×C4×C17C4⋊C416yes—
47C22×C4×C17C4⋊C4124yes—
48C22×C4×C17C4⋊C412yes—
49C22×C4×C17C4⋊C4112yes—
50C22×C4×C17C22×C411yescharacteristic
51C22×C4×C17C22×C413yes—
52C22×C4×C17C22×C4112yes—
53C22×C4×C17C22×C4112yes—
54C22×C4×C17C2×D4112yes—
55C22×C4×C17C2×D413yes—
56C22×C4×C17C2×D4112yes—
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×Q816yes—
59C22×C4×C17C2×Q8112yes—
60C22×C4×C17C2×Q813yes—
61C22×C4×C17C2413yes—
62C22×C4×C17C2414yes—
63M16×C17—232no—
64M16×C17—224no—
65M16×C17C22×C4164yes—
66M16×C17C24116yes—
67C2×C8×C17—224no—
68C2×C8×C17—232no—
69C2×C8×C17C22×C4124yes—
70C2×C8×C17C22×C4124yes—
71C2×C8×C17C2418yes—
72C22×#430C1711yesmaximal, characteristic, direct product factor, Sylow
73C23×C17—28no—
74C23×C17—24no—
75C23×C17—412no—
76C23×C17—412no—
77C23×C17C2×C4⋊C413yes—
78C23×C17C2×C4⋊C4112yes—
79C23×C17C2×C4⋊C4112yes—
80C23×C17C2×C4⋊C411yescharacteristic
81C23×C17C22×Q813yes—
82C23×C17C22×Q814yes—
83C2×C4×C17C2×C4⋊C416yes—
84C2×C4×C17C2×C4⋊C4124yes—
85C2×C4×C17C2×C4⋊C4124yes—
86C2×C4×C17C2×C4⋊C4112yes—
87C2×C4×C17C2×C4⋊C413yes—
88C2×C4×C17C2×C4⋊C4112yes—
89C2×C4×C17C2×C4⋊C413yes—
90C2×C4×C17C23×C413yes—
91C2×C4×C17C23×C413yes—
92C2×C4×C17C23×C418yes—
93C2×C4×C17C22×D413yes—
94C2×C4×C17C22×D418yes—
95C2×C4×C17C22×D413yes—
96C2×C4×C17C22×Q813yes—
97C2×C4×C17C22×Q814yes—
98C2×C4×C17C2511yescharacteristic
99C8×C17—216no—
100C8×C17C23×C4116yes—
101C23×M16C2×C1712yes—
102C23×M16C2×C1711yescharacteristic
103C2×#430C2×C17124yesdirect product factor
104C22×#108C2×C1714yescomplemented
105C22×C17—224no—
106C22×C17—26no—
107C22×C17—26no—
108C22×C17—412no—
109C22×C17—44no—
110C22×C17#43014yesdirect product factor
111C22×C17C22×C4⋊C413yes—
112C22×C17C22×C4⋊C418yes—
113C22×C17C22×C4⋊C413yes—
114C22×C17C23×Q811yescharacteristic
115C4×C17C22×C4⋊C413yes—
116C4×C17C22×C4⋊C418yes—
117C4×C17C22×C4⋊C413yes—
118C4×C17C24×C411yescharacteristic
119C4×C17C23×D411yescharacteristic
120C24×C4C22×C1711yescharacteristic
121C22×M16—22no—
122C22×M16—212no—
123C22×M16C4×C1714yes—
124C22×M16C4×C17112yes—
125C22×M16C22×C1714yes—
126C22×M16C22×C17124yes—
127C22×M16C22×C17112yes—
128C23×C8—22no—
129C23×C8C22×C1712yes—
130#430C22×C17164yesdirect product factor
131C2×#108C22×C17148yescomplemented
132C2×C17—28no—
133C2×C17—23no—
134C2×C17—21no—
135C2×C17C2×#43016yesdirect product factor
136C2×C17C23×C4⋊C411yescharacteristic
137C25Q8×C1711yescharacteristic
138C23×C4C2×C4×C1712yes—
139C23×C4C2×C4×C1716yes—
140C23×C4D4×C1712yes—
141C23×C4D4×C1716yes—
142C23×C4Q8×C1711yescharacteristic
143C23×C4Q8×C1716yes—
144C23×C4C23×C1711yescharacteristic
145C23×C4C23×C1716yes—
146C2×M16—224no—
147C2×M16—212no—
148C2×M16—248no—
149C2×M16C2×C4×C17148yes—
150C2×M16C2×C4×C17148yes—
151C2×M16C23×C17124yes—
152C2×M16C23×C17132yes—
153C2×M16C23×C17116yes—
154C22×C8—224no—
155C22×C8—24no—
156C22×C8C2×C4×C17112yes—
157C22×C8C2×C4×C1714yes—
158C22×C8C23×C17112yes—
159#108C23×C17164yescomplemented
160C17C22×#43011yescharacteristic, direct product factor, Sylow
161C24—44no—
162C24C4⋊C4×C1712yes—
163C24C4⋊C4×C1716yes—
164C24C2×Q8×C1711yescharacteristic
165C24C2×Q8×C1716yes—
166C22×C4C4⋊C4×C17112yes—
167C22×C4C4⋊C4×C17112yes—
168C22×C4C4⋊C4×C1716yes—
169C22×C4C4⋊C4×C17124yes—
170C22×C4C4⋊C4×C1712yes—
171C22×C4C22×C4×C1713yes—
172C22×C4C22×C4×C1711yescharacteristic
173C22×C4C22×C4×C17112yes—
174C22×C4C22×C4×C17112yes—
175C22×C4C2×D4×C17112yes—
176C22×C4C2×D4×C1713yes—
177C22×C4C2×D4×C17112yes—
178C22×C4C2×D4×C1711yescharacteristic
179C22×C4C2×Q8×C1713yes—
180C22×C4C2×Q8×C1716yes—
181C22×C4C2×Q8×C17112yes—
182C22×C4C24×C1713yes—
183C22×C4C24×C1714yes—
184M16—232no—
185M16—224no—
186M16C22×C4×C17164yes—
187M16C24×C17116yes—
188C2×C8—224no—
189C2×C8—232no—
190C2×C8C22×C4×C17124yes—
191C2×C8C22×C4×C17124yes—
192C2×C8C24×C1718yes—
193C23—28no—
194C23—24no—
195C23—412no—
196C23—412no—
197C23C2×C4⋊C4×C1713yes—
198C23C2×C4⋊C4×C17112yes—
199C23C2×C4⋊C4×C17112yes—
200C23C2×C4⋊C4×C1711yescharacteristic
201C23C22×Q8×C1713yes—
202C23C22×Q8×C1714yes—
203C2×C4C2×C4⋊C4×C1716yes—
204C2×C4C2×C4⋊C4×C17124yes—
205C2×C4C2×C4⋊C4×C17124yes—
206C2×C4C2×C4⋊C4×C17112yes—
207C2×C4C2×C4⋊C4×C1713yes—
208C2×C4C2×C4⋊C4×C1713yes—
209C2×C4C2×C4⋊C4×C17112yes—
210C2×C4C23×C4×C1713yes—
211C2×C4C23×C4×C1713yes—
212C2×C4C23×C4×C1718yes—
213C2×C4C22×D4×C1713yes—
214C2×C4C22×D4×C1718yes—
215C2×C4C22×D4×C1713yes—
216C2×C4C22×Q8×C1713yes—
217C2×C4C22×Q8×C1714yes—
218C2×C4C25×C1711yescharacteristic
219C8—216no—
220C8C23×C4×C17116yes—
221C22—26no—
222C22—224no—
223C22—26no—
224C22—44no—
225C22—412no—
226C22C17×#43014yesdirect product factor
227C22C22×C4⋊C4×C1713yes—
228C22C22×C4⋊C4×C1718yes—
229C22C22×C4⋊C4×C1713yes—
230C22C23×Q8×C1711yescharacteristic
231C4C22×C4⋊C4×C1713yes—
232C4C22×C4⋊C4×C1713yes—
233C4C22×C4⋊C4×C1718yes—
234C4C24×C4×C1711yescharacteristic
235C4C23×D4×C1711yescharacteristic
236C2—23no—
237C2—28no—
238C2—21no—
239C2C2×C17×#43016yesdirect product factor
240C2C23×C4⋊C4×C1711yescharacteristic
subgroupG/H
centerC22×C4×C17C2×D4
commutatorC4C24×C4×C17
Frattini, cosocleC2×C4C25×C17
socleC23×C17C2×C4⋊C4
prime radicalC25×C17Q8
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. C2×C17×#430C2direct (N × H)
4. C22×C17×#108C2semidirect
15. C17×#430C22direct (N × H)
16. C2×C17×#108C22semidirect
39. C17×#108C23semidirect
72. C22×#430C17direct (N × H)
103. C2×#430C2×C17direct (N × H)
104. C22×#108C2×C17semidirect
110. C22×C17#430direct (N × H)
130. #430C22×C17direct (N × H)
131. C2×#108C22×C17semidirect
135. C2×C17C2×#430direct (N × H)
159. #108C23×C17semidirect
160. C17C22×#430direct (N × H)
226. C22C17×#430direct (N × H)
239. C2C2×C17×#430direct (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
C2×C17×#4302
C22×C17×#1082
C22×#43017