Finite Group Databasebeta

← C17×#7495 #16865239

Subgroups — C17×#7495 #16865239

Order 4352.

280 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C2×C17×#355C211yesmaximal, characteristic
2C17×#1885C211yesmaximal, characteristic
3C17×#1533C211yesmaximal, characteristic
4C2×C17×#124C2211yescharacteristic
5C17×#518C411yescharacteristic
6C17×#432—21no—
7C17×#419—21no—
8C2×C17×#101—21no—
9C2×C17×#100C411yescharacteristic
10C17×#355—21no—
11C17×#355C412yescomplemented
12C17×#339—21no—
13C17×#329—21no—
14C17×#329C412yescomplemented
15C22×Q8×C17D411yescharacteristic
16C22×D4×C17C2×C411yescharacteristic
17C2×M16×C17—21no—
18C2×M16×C17—41no—
19C17×#124—41no—
20C17×#124C2×C411yescharacteristic
21C17×#124C2×C411yescharacteristic
22C17×#124D411yescharacteristic
23C17×#124Q811yescharacteristic
24C4×D4×C17—42no—
25C17×#117—21no—
26C2×C22⋊C4×C17—41no—
27C2×C22⋊C4×C17—41no—
28C2×C42×C17D411yescharacteristic
29C17×C4⋊C8—41no—
30C17×#103—42no—
31C17×#101—22no—
32C17×#101—41no—
33C17×#100—41no—
34C17×C22⋊C8—41no—
35C17×#97—22no—
36C24×C17—21no—
37C2×Q8×C17—21no—
38C2×Q8×C17—41no—
39C2×Q8×C17—41no—
40C2×Q8×C17C22⋊C411yescharacteristic
41C2×Q8×C17C4⋊C411yescharacteristic
42C2×D4×C17—21no—
43C2×D4×C17—41no—
44C2×D4×C17—41no—
45C2×D4×C17C4211yescharacteristic
46C2×D4×C17C4⋊C411yescharacteristic
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17—42no—
50C22×C4×C17C22⋊C411yescharacteristic
51M16×C17—41no—
52M16×C17—42no—
53M16×C17—41no—
54M16×C17—81no—
55C2×C8×C17—41no—
56C2×C8×C17—42no—
57C2×C8×C17—81no—
58C4⋊C4×C17—22no—
59C22⋊C4×C17—41no—
60C22⋊C4×C17—41no—
61C22⋊C4×C17—41no—
62C22⋊C4×C17—41no—
63C22⋊C4×C17—41no—
64C22⋊C4×C17—42no—
65C42×C17—21no—
66C42×C17—41no—
67C42×C17C22⋊C411yescharacteristic
68C42×C17C4⋊C411yescharacteristic
69#7495C1711yesmaximal, characteristic, direct product factor, Sylow
70C23×C17—21no—
71C23×C17—21no—
72C23×C17—41no—
73C23×C17—41no—
74C23×C17—82no—
75C23×C17#9911yescharacteristic
76Q8×C17—41no—
77Q8×C17—41no—
78Q8×C17—81no—
79D4×C17—41no—
80D4×C17—41no—
81D4×C17—42no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—42no—
91C2×C4×C17—81no—
92C2×C4×C17—162no—
93C2×C4×C17#9511yescharacteristic
94C2×C4×C17#9911yescharacteristic
95C8×C17—81no—
96C8×C17—82no—
97C8×C17—82no—
98C2×#355C2×C1711yescharacteristic
99#1885C2×C1711yescharacteristic
100#1533C2×C1711yescharacteristic
101C22×C17—41no—
102C22×C17—41no—
103C22×C17—41no—
104C22×C17—81no—
105C22×C17—81no—
106C22×C17—82no—
107C22×C17—161no—
108C22×C17#34211yescharacteristic
109C22×C17AΣL(1,𝔽16)11yescharacteristic
110C22×C17#35211yescharacteristic
111C4×C17—21no—
112C4×C17—21no—
113C4×C17—41no—
114C4×C17—41no—
115C4×C17—41no—
116C4×C17—41no—
117C4×C17—82no—
118C2×#124C22×C1711yescharacteristic
119#518C4×C1711yescharacteristic
120#432—21no—
121#419—21no—
122C2×#101—21no—
123C2×#100C4×C1711yescharacteristic
124#355—21no—
125#355C4×C1712yescomplemented
126#339—21no—
127#329—21no—
128#329C4×C1712yescomplemented
129C2×C17—21no—
130C2×C17—21no—
131C2×C17—21no—
132C2×C17—81no—
133C2×C17—81no—
134C2×C17#139011yescharacteristic
135C22×Q8D4×C1711yescharacteristic
136C22×D4C2×C4×C1711yescharacteristic
137C2×M16—21no—
138C2×M16—41no—
139#124—41no—
140#124C2×C4×C1711yescharacteristic
141#124C2×C4×C1711yescharacteristic
142#124D4×C1711yescharacteristic
143#124Q8×C1711yescharacteristic
144C4×D4—42no—
145#117—21no—
146C2×C22⋊C4—41no—
147C2×C22⋊C4—41no—
148C2×C42D4×C1711yescharacteristic
149C4⋊C8—41no—
150#103—42no—
151#101—22no—
152#101—41no—
153#100—41no—
154C22⋊C8—41no—
155#97—22no—
156C17#749511yescharacteristic, direct product factor, Sylow
157C24—21no—
158C2×Q8—21no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8C22⋊C4×C1711yescharacteristic
162C2×Q8C4⋊C4×C1711yescharacteristic
163C2×D4—21no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4C42×C1711yescharacteristic
167C2×D4C4⋊C4×C1711yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—42no—
171C22×C4C22⋊C4×C1711yescharacteristic
172M16—42no—
173M16—41no—
174M16—41no—
175M16—81no—
176C2×C8—42no—
177C2×C8—41no—
178C2×C8—81no—
179C4⋊C4—22no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—42no—
186C42—21no—
187C42—41no—
188C42C22⋊C4×C1711yescharacteristic
189C42C4⋊C4×C1711yescharacteristic
190C23—21no—
191C23—21no—
192C23—41no—
193C23—41no—
194C23—82no—
195C23C17×#9911yescharacteristic
196Q8—41no—
197Q8—41no—
198Q8—81no—
199D4—41no—
200D4—41no—
201D4—42no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—81no—
212C2×C4—162no—
213C2×C4C17×#9511yescharacteristic
214C2×C4C17×#9911yescharacteristic
215C8—81no—
216C8—82no—
217C8—82no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—81no—
222C22—81no—
223C22—82no—
224C22—161no—
225C22C17×#34211yescharacteristic
226C22C17×AΣL(1,𝔽16)11yescharacteristic
227C22C17×#35211yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—82no—
235C2—21no—
236C2—21no—
237C2—21no—
238C2—81no—
239C2—81no—
240C2C17×#139011yescharacteristic
subgroupG/H
center, socleC2×C17#1390
commutatorC2×D4C42×C17
Frattini, cosocleC2×#124C22×C17
prime radicalC22×D4×C17C2×C4
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C17 ◁ C23×C17 ◁ C22×C4×C17 ◁ C2×C17×#124 ◁ G

Complements

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

NH ≅ G/Ntype
11. C17×#355C4semidirect
14. C17×#329C4semidirect
69. #7495C17direct (N × H)
125. #355C4×C17semidirect
128. #329C4×C17semidirect
156. C17#7495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#3552
C17×#18852
C17×#15332
#749517