Finite Group Databasebeta

← C17×#11197 #16868941

Subgroups — C17×#11197 #16868941

Order 4352.

1134 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 238 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×#381C212yesmaximal
2C2×C17×#381C211yesmaximal, characteristic
3C2×C17×#342C214yesmaximal
4C24×C4×C17C2211yescharacteristic
5C22×C22⋊C4×C17C2214yes—
6C22×C22⋊C4×C17C2212yes—
7C17×#381—28no—
8C17×#381—24no—
9C2×C17×#95—24no—
10C2×C17×#95C414yescomplemented
11C17×#342—28no—
12C25×C17C2311yescharacteristic
13C23×C4×C17—24no—
14C23×C4×C17—24no—
15C23×C4×C17—24no—
16C23×C4×C17—24no—
17C23×C4×C17C2×C412yes—
18C23×C4×C17C2×C414yes—
19C23×C4×C17D414yes—
20C2×C22⋊C4×C17—24no—
21C2×C22⋊C4×C17—24no—
22C2×C22⋊C4×C17—24no—
23C2×C22⋊C4×C17—24no—
24C2×C22⋊C4×C17—24no—
25C2×C22⋊C4×C17—22no—
26C2×C22⋊C4×C17—22no—
27C2×C22⋊C4×C17—24no—
28C2×C22⋊C4×C17—24no—
29C2×C22⋊C4×C17D418yes—
30C17×#95—216no—
31C17×#95—28no—
32C24×C17—44no—
33C24×C17C22×C411yescharacteristic
34C24×C17C2×D412yes—
35C24×C17C2×D414yes—
36C24×C17#4114yes—
37C24×C17#4114yes—
38C22×C4×C17—24no—
39C22×C4×C17—28no—
40C22×C4×C17—24no—
41C22×C4×C17—28no—
42C22×C4×C17—28no—
43C22×C4×C17—24no—
44C22×C4×C17—24no—
45C22×C4×C17—28no—
46C22×C4×C17—28no—
47C22×C4×C17—44no—
48C22×C4×C17—44no—
49C22×C4×C17—44no—
50C22×C4×C17—44no—
51C22×C4×C17—416no—
52C22×C4×C17—44no—
53C22×C4×C17—44no—
54C22×C4×C17—48no—
55C22×C4×C17C22⋊C414yes—
56C22⋊C4×C17—28no—
57C22⋊C4×C17—28no—
58C22⋊C4×C17—42no—
59C22⋊C4×C17—44no—
60C22⋊C4×C17—44no—
61C22⋊C4×C17—42no—
62C22⋊C4×C17—44no—
63#11197C1711yesmaximal, characteristic, direct product factor, Sylow
64C23×C17—24no—
65C23×C17—28no—
66C23×C17—48no—
67C23×C17—48no—
68C23×C17—48no—
69C23×C17C2×C22⋊C411yescharacteristic
70C23×C17#11712yes—
71C23×C17C4×D414yes—
72C23×C17#12012yes—
73C23×C17#12114yes—
74C23×C17#12114yes—
75C23×C17#12314yes—
76C23×C17#12312yes—
77C23×C17#12314yes—
78C23×C17#12414yes—
79C23×C17#12614yes—
80C2×C4×C17—24no—
81C2×C4×C17—28no—
82C2×C4×C17—48no—
83C2×C4×C17—48no—
84C2×C4×C17—48no—
85C2×C4×C17—416no—
86C2×C4×C17—44no—
87C2×C4×C17—48no—
88C2×C4×C17—48no—
89C2×C4×C17—88no—
90C2×C4×C17—88no—
91C2×C4×C17—88no—
92C2×#381C2×C1712yes—
93C2×#381C2×C1711yescharacteristic
94C2×#342C2×C1714yes—
95C22×C17—28no—
96C22×C17—24no—
97C22×C17—24no—
98C22×C17—28no—
99C22×C17—28no—
100C22×C17—24no—
101C22×C17—44no—
102C22×C17—44no—
103C22×C17—44no—
104C22×C17—44no—
105C22×C17#38111yescharacteristic
106C22×C17#38612yes—
107C22×C17#38814yes—
108C22×C17#39414yes—
109C22×C17#39714yes—
110C22×C17#41014yes—
111C4×C17—44no—
112C4×C17—88no—
113C4×C17—84no—
114C24×C4C22×C1711yescharacteristic
115C22×C22⋊C4C22×C1712yes—
116C22×C22⋊C4C22×C1714yes—
117#381—24no—
118#381—28no—
119C2×#95—24no—
120C2×#95C4×C1714yescomplemented
121#342—28no—
122C2×C17—24no—
123C2×C17—24no—
124C2×C17—24no—
125C2×C17#144011yescharacteristic
126C2×C17#182012yes—
127C2×C17#189914yes—
128C25C23×C1711yescharacteristic
129C23×C4—24no—
130C23×C4—24no—
131C23×C4—24no—
132C23×C4—24no—
133C23×C4C2×C4×C1712yes—
134C23×C4C2×C4×C1714yes—
135C23×C4D4×C1714yes—
136C2×C22⋊C4—24no—
137C2×C22⋊C4—24no—
138C2×C22⋊C4—24no—
139C2×C22⋊C4—24no—
140C2×C22⋊C4—24no—
141C2×C22⋊C4—22no—
142C2×C22⋊C4—24no—
143C2×C22⋊C4—22no—
144C2×C22⋊C4—24no—
145C2×C22⋊C4D4×C1718yes—
146#95—216no—
147#95—28no—
148C17#1119711yescharacteristic, direct product factor, Sylow
149C24—44no—
150C24C22×C4×C1711yescharacteristic
151C24C2×D4×C1712yes—
152C24C2×D4×C1714yes—
153C24#41×C1714yes—
154C24#41×C1714yes—
155C22×C4—28no—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—28no—
159C22×C4—24no—
160C22×C4—28no—
161C22×C4—24no—
162C22×C4—28no—
163C22×C4—28no—
164C22×C4—44no—
165C22×C4—44no—
166C22×C4—44no—
167C22×C4—44no—
168C22×C4—416no—
169C22×C4—44no—
170C22×C4—44no—
171C22×C4—48no—
172C22×C4C22⋊C4×C1714yes—
173C22⋊C4—28no—
174C22⋊C4—28no—
175C22⋊C4—42no—
176C22⋊C4—44no—
177C22⋊C4—42no—
178C22⋊C4—44no—
179C22⋊C4—44no—
180C23—24no—
181C23—28no—
182C23—48no—
183C23—48no—
184C23—48no—
185C23C2×C22⋊C4×C1711yescharacteristic
186C23C17×#11712yes—
187C23C4×D4×C1714yes—
188C23C17×#12012yes—
189C23C17×#12114yes—
190C23C17×#12114yes—
191C23C17×#12314yes—
192C23C17×#12312yes—
193C23C17×#12314yes—
194C23C17×#12414yes—
195C23C17×#12614yes—
196C2×C4—24no—
197C2×C4—28no—
198C2×C4—48no—
199C2×C4—48no—
200C2×C4—48no—
201C2×C4—416no—
202C2×C4—44no—
203C2×C4—48no—
204C2×C4—48no—
205C2×C4—88no—
206C2×C4—88no—
207C2×C4—88no—
208C22—28no—
209C22—24no—
210C22—24no—
211C22—28no—
212C22—28no—
213C22—24no—
214C22—44no—
215C22—44no—
216C22—44no—
217C22—44no—
218C22C17×#38111yescharacteristic
219C22C17×#38612yes—
220C22C17×#38814yes—
221C22C17×#39414yes—
222C22C17×#39714yes—
223C22C17×#41014yes—
224C4—44no—
225C4—88no—
226C4—84no—
227C2—24no—
228C2—24no—
229C2—24no—
230C2C17×#144011yescharacteristic
231C2C17×#182012yes—
232C2C17×#189914yes—
subgroupG/H
center, socleC23×C17C2×C22⋊C4
commutatorC24C22×C4×C17
Frattini, cosocleC25C23×C17
prime radicalC25×C17C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C17 ◁ C24×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
10. C2×C17×#95C4semidirect
63. #11197C17direct (N × H)
120. C2×#95C4×C17semidirect
148. C17#11197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#3812
C2×C17×#3422
#1119717