Finite Group Databasebeta

← C17×#7629 #16865373

Subgroups — C17×#7629 #16865373

Order 4352.

658 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 150 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×#391C211yesmaximal, characteristic
2C17×#1749C212yesmaximal
3C17×#1272C214yesmaximal, complemented
4C23×Q8×C17C411yescharacteristic
5C22×C4⋊C4×C17C411yescharacteristic
6C22×C42×C17C2211yescharacteristic
7C2×C17×C22⋊C8—22no—
8C2×C17×#97—22no—
9C17×#391—22no—
10C17×#391C412yes—
11C17×#391C2212yes—
12C2×C17×#95—22no—
13C17×#336C2214yes—
14C22×Q8×C17—24no—
15C22×Q8×C17—21no—
16C22×Q8×C17—42no—
17C22×Q8×C17—42no—
18C22×Q8×C17C2×C412yes—
19C23×C4×C17—21no—
20C23×C4×C17—21no—
21C23×C4×C17C2×C411yescharacteristic
22C23×C4×C17D412yes—
23C22×C8×C17—24no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17—42no—
26C2×C4⋊C4×C17C2×C412yes—
27C2×C42×C17—42no—
28C2×C42×C17C2×C411yescharacteristic
29C2×C42×C17D412yes—
30C2×C42×C17C2311yescharacteristic
31C17×C22⋊C8—28no—
32C17×#97—44no—
33C17×#95—24no—
34C17×#95—24no—
35C24×C17C22⋊C411yescharacteristic
36C2×Q8×C17—24no—
37C2×Q8×C17—22no—
38C2×Q8×C17—416no—
39C2×Q8×C17—42no—
40C2×Q8×C17—42no—
41C2×Q8×C17—42no—
42C2×Q8×C17—42no—
43C2×Q8×C17M1614yes—
44C22×C4×C17—22no—
45C22×C4×C17—22no—
46C22×C4×C17—22no—
47C22×C4×C17—24no—
48C22×C4×C17—24no—
49C22×C4×C17—22no—
50C22×C4×C17—24no—
51C22×C4×C17—22no—
52C22×C4×C17—42no—
53C22×C4×C17—42no—
54C22×C4×C17—42no—
55C22×C4×C17—42no—
56C22×C4×C17—44no—
57C22×C4×C17C22⋊C412yes—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C22×C4×C17C2×D412yes—
61C2×C8×C17—28no—
62C2×C8×C17—44no—
63C2×C8×C17—44no—
64C4⋊C4×C17—42no—
65C4⋊C4×C17—42no—
66C42×C17—24no—
67C42×C17—41no—
68C42×C17—41no—
69#7629C1711yesmaximal, characteristic, direct product factor, Sylow
70C23×C17—21no—
71C23×C17—21no—
72C23×C17—22no—
73C23×C17#10012yes—
74C23×C17#10414yes—
75C23×C17C2×C22⋊C411yescharacteristic
76Q8×C17—44no—
77Q8×C17—48no—
78Q8×C17—44no—
79C2×C4×C17—28no—
80C2×C4×C17—21no—
81C2×C4×C17—22no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—22no—
86C2×C4×C17—24no—
87C2×C4×C17—22no—
88C2×C4×C17—22no—
89C2×C4×C17—22no—
90C2×C4×C17—48no—
91C2×C4×C17—48no—
92C2×C4×C17—42no—
93C2×C4×C17—42no—
94C2×C4×C17—42no—
95C2×C4×C17—44no—
96C2×C4×C17—84no—
97C2×C4×C17#9912yes—
98C2×C4×C17C2×M1612yes—
99C2×C4×C17#13714yes—
100C8×C17—48no—
101C2×#391C2×C1711yescharacteristic
102#1749C2×C1712yes—
103#1272C2×C1714yescomplemented
104C22×C17—22no—
105C22×C17—22no—
106C22×C17—24no—
107C22×C17—24no—
108C22×C17#32914yes—
109C22×C17#40711yescharacteristic
110C22×C17C2×#9911yescharacteristic
111C22×C17C2×#10011yescharacteristic
112C22×C17#41912yes—
113C22×C17C2×#10412yes—
114C4×C17—22no—
115C4×C17—22no—
116C4×C17—24no—
117C4×C17—44no—
118C4×C17—42no—
119C4×C17—82no—
120C23×Q8C4×C1711yescharacteristic
121C22×C4⋊C4C4×C1711yescharacteristic
122C22×C42C22×C1711yescharacteristic
123C2×C22⋊C8—22no—
124C2×#97—22no—
125#391—22no—
126#391C4×C1712yes—
127#391C22×C1712yes—
128C2×#95—22no—
129#336C22×C1714yes—
130C2×C17—24no—
131C2×C17#146211yescharacteristic
132C2×C17#149112yes—
133C2×C17#150812yes—
134C2×C17C2×#32911yescharacteristic
135C2×C17#155811yescharacteristic
136C22×Q8—24no—
137C22×Q8—21no—
138C22×Q8—42no—
139C22×Q8—42no—
140C22×Q8C2×C4×C1712yes—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4C2×C4×C1711yescharacteristic
144C23×C4D4×C1712yes—
145C22×C8—24no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4C2×C4×C1712yes—
149C2×C42—42no—
150C2×C42C2×C4×C1711yescharacteristic
151C2×C42D4×C1712yes—
152C2×C42C23×C1711yescharacteristic
153C22⋊C8—28no—
154#97—44no—
155#95—24no—
156#95—24no—
157C17#762911yescharacteristic, direct product factor, Sylow
158C24C22⋊C4×C1711yescharacteristic
159C2×Q8—24no—
160C2×Q8—22no—
161C2×Q8—416no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8M16×C1714yes—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—24no—
171C22×C4—24no—
172C22×C4—22no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—44no—
180C22×C4C22⋊C4×C1712yes—
181C22×C4C22⋊C4×C1711yescharacteristic
182C22×C4C22×C4×C1711yescharacteristic
183C22×C4C2×D4×C1712yes—
184C2×C8—28no—
185C2×C8—44no—
186C2×C8—44no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C42—24no—
190C42—41no—
191C42—41no—
192C23—21no—
193C23—21no—
194C23—22no—
195C23C17×#10012yes—
196C23C17×#10414yes—
197C23C2×C22⋊C4×C1711yescharacteristic
198Q8—44no—
199Q8—44no—
200Q8—48no—
201C2×C4—28no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—48no—
213C2×C4—48no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—44no—
218C2×C4—84no—
219C2×C4C17×#9912yes—
220C2×C4C2×M16×C1712yes—
221C2×C4C17×#13714yes—
222C8—48no—
223C22—22no—
224C22—24no—
225C22—24no—
226C22—22no—
227C22C17×#32914yes—
228C22C17×#40711yescharacteristic
229C22C2×C17×#9911yescharacteristic
230C22C2×C17×#10011yescharacteristic
231C22C17×#41912yes—
232C22C2×C17×#10412yes—
233C4—22no—
234C4—22no—
235C4—24no—
236C4—44no—
237C4—42no—
238C4—82no—
239C2—24no—
240C2C17×#146211yescharacteristic
241C2C17×#149112yes—
242C2C17×#150812yes—
243C2C2×C17×#32911yescharacteristic
244C2C17×#155811yescharacteristic
subgroupG/H
center, socleC23×C17C2×C22⋊C4
commutatorC22×C4C22×C4×C17
Frattini, cosocleC2×C42C23×C17
prime radicalC24×C17C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
3. C17×#1272C2semidirect
69. #7629C17direct (N × H)
103. #1272C2×C17semidirect
157. C17#7629direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#3912
C17×#17492
C17×#12722
#762917