Finite Group Databasebeta

← C17×#11504 #16869248

Subgroups — C17×#11504 #16869248

Order 4352.

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

normal subgroups only

This group has 510 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×#2310C211yesmaximal, characteristic
2C17×#1464C212yesmaximal
3C17×#1317C214yesmaximal
4C23×Q8×C17C411yescharacteristic
5C2×C17×#117C411yescharacteristic
6C2×C17×#117C2211yescharacteristic
7C17×#432—22no—
8C17×#391—22no—
9C17×#391—22no—
10C17×#381C412yes—
11C17×#381C2212yes—
12C17×#324—22no—
13C17×#323C2214yes—
14C22×Q8×C17—21no—
15C22×Q8×C17—21no—
16C22×Q8×C17—24no—
17C22×Q8×C17—41no—
18C22×Q8×C17—41no—
19C22×Q8×C17—42no—
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C412yes—
22C17×#117—41no—
23C17×#117—41no—
24C17×#117—42no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17D412yes—
27C2×C22⋊C4×C17C2×C412yes—
28C2×C22⋊C4×C17C2×C411yescharacteristic
29C2×C22⋊C4×C17C2311yescharacteristic
30C2×C42×C17—21no—
31C2×C42×C17D412yes—
32C17×C4⋊C8—42no—
33C17×C22⋊C8—24no—
34C17×#97—42no—
35C17×#95—24no—
36C17×#95—24no—
37C24×C17C22×C411yescharacteristic
38C2×Q8×C17—24no—
39C2×Q8×C17—24no—
40C2×Q8×C17—48no—
41C2×Q8×C17—48no—
42C2×Q8×C17—42no—
43C2×Q8×C17—42no—
44C2×Q8×C17—41no—
45C2×Q8×C17—41no—
46C2×Q8×C17—42no—
47C22×C4×C17—22no—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17—22no—
51C22×C4×C17—22no—
52C22×C4×C17—22no—
53C22×C4×C17—22no—
54C22×C4×C17—42no—
55C22×C4×C17—42no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C412yes—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17M1614yes—
60C22×C4×C17C2×D412yes—
61C2×C8×C17—44no—
62C4⋊C4×C17—42no—
63C4⋊C4×C17—42no—
64C22⋊C4×C17—41no—
65C22⋊C4×C17—41no—
66C22⋊C4×C17—42no—
67C42×C17—22no—
68C42×C17—22no—
69C42×C17—42no—
70#11504C1711yesmaximal, characteristic, direct product factor, Sylow
71C23×C17—21no—
72C23×C17—21no—
73C23×C17—42no—
74C23×C17C2×C22⋊C411yescharacteristic
75C23×C17C2×M1612yes—
76Q8×C17—44no—
77Q8×C17—44no—
78Q8×C17—48no—
79C2×C4×C17—24no—
80C2×C4×C17—24no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—24no—
86C2×C4×C17—22no—
87C2×C4×C17—22no—
88C2×C4×C17—44no—
89C2×C4×C17—42no—
90C2×C4×C17—42no—
91C2×C4×C17—44no—
92C2×C4×C17—42no—
93C2×C4×C17—42no—
94C2×C4×C17—44no—
95C2×C4×C17—42no—
96C2×C4×C17#9911yescharacteristic
97C2×C4×C17#9911yescharacteristic
98C2×C4×C17#10012yes—
99C8×C17—84no—
100#2310C2×C1711yescharacteristic
101#1464C2×C1712yes—
102#1317C2×C1714yes—
103C22×C17—22no—
104C22×C17—22no—
105C22×C17—42no—
106C22×C17—42no—
107C22×C17—42no—
108C22×C17#40711yescharacteristic
109C22×C17C2×#9911yescharacteristic
110C22×C17C2×#10011yescharacteristic
111C4×C17—21no—
112C4×C17—21no—
113C4×C17—22no—
114C4×C17—42no—
115C4×C17—42no—
116C4×C17—44no—
117C4×C17—82no—
118C23×Q8C4×C1711yescharacteristic
119C2×#117C4×C1711yescharacteristic
120C2×#117C22×C1711yescharacteristic
121#432—22no—
122#391—22no—
123#391—22no—
124#381C4×C1712yes—
125#381C22×C1712yes—
126#324—22no—
127#323C22×C1714yes—
128C2×C17—21no—
129C2×C17—21no—
130C2×C17—42no—
131C2×C17#146211yescharacteristic
132C2×C17#212312yes—
133C22×Q8—21no—
134C22×Q8—21no—
135C22×Q8—24no—
136C22×Q8—41no—
137C22×Q8—41no—
138C22×Q8—42no—
139C23×C4C2×C4×C1711yescharacteristic
140C23×C4C2×C4×C1712yes—
141#117—41no—
142#117—41no—
143#117—42no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4D4×C1712yes—
146C2×C22⋊C4C2×C4×C1712yes—
147C2×C22⋊C4C2×C4×C1711yescharacteristic
148C2×C22⋊C4C23×C1711yescharacteristic
149C2×C42—21no—
150C2×C42D4×C1712yes—
151C4⋊C8—42no—
152C22⋊C8—24no—
153#97—42no—
154#95—24no—
155#95—24no—
156C17#1150411yescharacteristic, direct product factor, Sylow
157C24C22×C4×C1711yescharacteristic
158C2×Q8—24no—
159C2×Q8—24no—
160C2×Q8—48no—
161C2×Q8—48no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—42no—
167C22×C4—22no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4C22⋊C4×C1711yescharacteristic
177C22×C4C22⋊C4×C1711yescharacteristic
178C22×C4C22⋊C4×C1712yes—
179C22×C4M16×C1714yes—
180C22×C4C2×D4×C1712yes—
181C2×C8—44no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—42no—
187C42—22no—
188C42—22no—
189C42—42no—
190C23—21no—
191C23—21no—
192C23—42no—
193C23C2×C22⋊C4×C1711yescharacteristic
194C23C2×M16×C1712yes—
195Q8—44no—
196Q8—44no—
197Q8—48no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—44no—
214C2×C4—42no—
215C2×C4C17×#9911yescharacteristic
216C2×C4C17×#9911yescharacteristic
217C2×C4C17×#10012yes—
218C8—84no—
219C22—22no—
220C22—22no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C17×#40711yescharacteristic
225C22C2×C17×#9911yescharacteristic
226C22C2×C17×#10011yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—44no—
231C4—42no—
232C4—42no—
233C4—82no—
234C2—21no—
235C2—21no—
236C2—42no—
237C2C17×#146211yescharacteristic
238C2C17×#212312yes—
subgroupG/H
center, socleC22×C17C2×#99
commutatorC24C22×C4×C17
Frattini, cosocleC2×C22⋊C4C23×C17
prime radicalC24×C17C22×C4
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
70. #11504C17direct (N × H)
156. C17#11504direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#23102
C17×#14642
C17×#13172
#1150417