Finite Group Databasebeta

← C17×#7632 #16865376

Subgroups — C17×#7632 #16865376

Order 4352.

590 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2296C211yesmaximal, characteristic
2C17×#1728C212yesmaximal
3C17×#1271C214yesmaximal, complemented
4C22×M16×C17—22no—
5C2×C17×#117C411yescharacteristic
6C2×C17×#117C411yescharacteristic
7C22×C42×C17C2211yescharacteristic
8C17×#389C412yes—
9C17×#389C2212yes—
10C17×#385—22no—
11C4×C4⋊C4×C17—22no—
12C17×#336—22no—
13C17×#336C2214yes—
14C23×C4×C17C2×C411yescharacteristic
15C23×C4×C17D412yes—
16C2×M16×C17—28no—
17C2×M16×C17—44no—
18C2×M16×C17—44no—
19C22×C8×C17—24no—
20C17×#117—24no—
21C17×#117—42no—
22C2×C4⋊C4×C17—22no—
23C2×C4⋊C4×C17—22no—
24C2×C4⋊C4×C17C2×C412yes—
25C2×C4⋊C4×C17C2×C412yes—
26C2×C22⋊C4×C17—21no—
27C2×C22⋊C4×C17—21no—
28C2×C42×C17—21no—
29C2×C42×C17—21no—
30C2×C42×C17—42no—
31C2×C42×C17C2×C411yescharacteristic
32C2×C42×C17D412yes—
33C2×C42×C17C2311yescharacteristic
34C17×#95—22no—
35C17×#95—22no—
36C24×C17C22⋊C411yescharacteristic
37C22×C4×C17—24no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—24no—
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17—22no—
44C22×C4×C17—22no—
45C22×C4×C17—22no—
46C22×C4×C17C22⋊C411yescharacteristic
47C22×C4×C17C22⋊C412yes—
48C22×C4×C17C22×C411yescharacteristic
49C22×C4×C17C2×D412yes—
50M16×C17—416no—
51C2×C8×C17—28no—
52C2×C8×C17—44no—
53C2×C8×C17—44no—
54C4⋊C4×C17—22no—
55C4⋊C4×C17—42no—
56C4⋊C4×C17—44no—
57C4⋊C4×C17—42no—
58C4⋊C4×C17—42no—
59C4⋊C4×C17M1614yescomplemented
60C22⋊C4×C17—24no—
61C22⋊C4×C17—42no—
62C42×C17—24no—
63C42×C17—41no—
64C42×C17—42no—
65C42×C17—41no—
66C42×C17—42no—
67#7632C1711yesmaximal, characteristic, direct product factor, Sylow
68C23×C17—21no—
69C23×C17—21no—
70C23×C17—22no—
71C23×C17—22no—
72C23×C17#9912yes—
73C23×C17C2×C22⋊C411yescharacteristic
74C2×C4×C17—28no—
75C2×C4×C17—28no—
76C2×C4×C17—28no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—22no—
81C2×C4×C17—22no—
82C2×C4×C17—21no—
83C2×C4×C17—22no—
84C2×C4×C17—22no—
85C2×C4×C17—24no—
86C2×C4×C17—42no—
87C2×C4×C17—42no—
88C2×C4×C17—42no—
89C2×C4×C17—42no—
90C2×C4×C17—42no—
91C2×C4×C17#10112yes—
92C2×C4×C17#10414yes—
93C2×C4×C17C2×M1612yes—
94C2×C4×C17AGL(1,ℤ/8)12yes—
95C2×C4×C17#13712yes—
96C8×C17—48no—
97#2296C2×C1711yescharacteristic
98#1728C2×C1712yes—
99#1271C2×C1714yescomplemented
100C22×C17—22no—
101C22×C17—24no—
102C22×C17—41no—
103C22×C17—42no—
104C22×C17—41no—
105C22×C17#40711yescharacteristic
106C22×C17C2×#9911yescharacteristic
107C22×C17C2×#10111yescharacteristic
108C22×C17#41712yes—
109C22×C17C2×#10412yes—
110C4×C17—22no—
111C4×C17—22no—
112C4×C17—22no—
113C4×C17—24no—
114C4×C17—22no—
115C4×C17—44no—
116C4×C17—82no—
117C22×M16—22no—
118C2×#117C4×C1711yescharacteristic
119C2×#117C4×C1711yescharacteristic
120C22×C42C22×C1711yescharacteristic
121#389C4×C1712yes—
122#389C22×C1712yes—
123#385—22no—
124C4×C4⋊C4—22no—
125#336—22no—
126#336C22×C1714yes—
127C2×C17—42no—
128C2×C17#146311yescharacteristic
129C2×C17#148912yes—
130C2×C17#150412yes—
131C2×C17#152611yescharacteristic
132C2×C17#156111yescharacteristic
133C23×C4C2×C4×C1711yescharacteristic
134C23×C4D4×C1712yes—
135C2×M16—28no—
136C2×M16—44no—
137C2×M16—44no—
138C22×C8—24no—
139#117—24no—
140#117—42no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4C2×C4×C1712yes—
144C2×C4⋊C4C2×C4×C1712yes—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—21no—
147C2×C42—21no—
148C2×C42—21no—
149C2×C42—42no—
150C2×C42C2×C4×C1711yescharacteristic
151C2×C42D4×C1712yes—
152C2×C42C23×C1711yescharacteristic
153#95—22no—
154#95—22no—
155C17#763211yescharacteristic, direct product factor, Sylow
156C24C22⋊C4×C1711yescharacteristic
157C22×C4—22no—
158C22×C4—24no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4C22⋊C4×C1711yescharacteristic
167C22×C4C22⋊C4×C1712yes—
168C22×C4C22×C4×C1711yescharacteristic
169C22×C4C2×D4×C1712yes—
170M16—416no—
171C2×C8—28no—
172C2×C8—44no—
173C2×C8—44no—
174C4⋊C4—22no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4—44no—
179C4⋊C4M16×C1714yescomplemented
180C22⋊C4—24no—
181C22⋊C4—42no—
182C42—24no—
183C42—41no—
184C42—42no—
185C42—41no—
186C42—42no—
187C23—21no—
188C23—21no—
189C23—22no—
190C23—22no—
191C23C17×#9912yes—
192C23C2×C22⋊C4×C1711yescharacteristic
193C2×C4—28no—
194C2×C4—28no—
195C2×C4—28no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4C17×#10112yes—
211C2×C4C17×#10414yes—
212C2×C4C2×M16×C1712yes—
213C2×C4C17×AGL(1,ℤ/8)12yes—
214C2×C4C17×#13712yes—
215C8—48no—
216C22—22no—
217C22—24no—
218C22—42no—
219C22—41no—
220C22—41no—
221C22C17×#40711yescharacteristic
222C22C2×C17×#9911yescharacteristic
223C22C2×C17×#10111yescharacteristic
224C22C17×#41712yes—
225C22C2×C17×#10412yes—
226C4—22no—
227C4—22no—
228C4—22no—
229C4—22no—
230C4—24no—
231C4—44no—
232C4—82no—
233C2—42no—
234C2C17×#146311yescharacteristic
235C2C17×#148912yes—
236C2C17×#150412yes—
237C2C17×#152611yescharacteristic
238C2C17×#156111yescharacteristic
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×#1271C2semidirect
59. C4⋊C4×C17M16semidirect
67. #7632C17direct (N × H)
99. #1271C2×C17semidirect
155. C17#7632direct (N × H)
179. C4⋊C4M16×C17semidirect

Maximal subgroups

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

subgroupindex
C17×#22962
C17×#17282
C17×#12712
#763217