Finite Group Databasebeta

← C17×#21827 #16879571

Subgroups — C17×#21827 #16879571

Order 4352.

1130 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 366 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×#543C211yesmaximal, characteristic
2C17×#2312C212yesmaximal
3C17×#1996C218yesmaximal, complemented
4C17×#1819C214yesmaximal
5C17×#543—28no—
6C2×C17×C22⋊Q8C418yescomplemented
7C2×C17×C22⋊Q8C2214yes—
8C22×C22⋊C4×C17C2212yes—
9C22×C22⋊C4×C17C2211yescharacteristic
10C17×#388—28no—
11C17×#380C2214yes—
12C17×#379C2214yes—
13C4×C22⋊C4×C17C2214yes—
14C17×#342C22116yes—
15C25×C17C2311yescharacteristic
16C22×Q8×C17C2×C414yes—
17C23×C4×C17C2×C414yes—
18C23×C4×C17C2312yes—
19C17×C22⋊Q8—28no—
20C17×C22⋊Q8—28no—
21C17×C22⋊Q8—232no—
22C2×C4⋊C4×C17—24no—
23C2×C4⋊C4×C17C2×C4112yes—
24C2×C22⋊C4×C17—28no—
25C2×C22⋊C4×C17—24no—
26C2×C22⋊C4×C17—24no—
27C2×C22⋊C4×C17C2×C414yes—
28C2×C22⋊C4×C17C2×C414yes—
29C2×C22⋊C4×C17D418yes—
30C2×C22⋊C4×C17C2318yes—
31C2×C22⋊C4×C17C2314yes—
32C2×C42×C17—24no—
33C17×#95—24no—
34C17×#95—24no—
35C24×C17—24no—
36C24×C17—82no—
37C24×C17C22×C412yes—
38C24×C17C2×D414yes—
39C24×C17C2411yescharacteristic
40C2×Q8×C17—28no—
41C2×Q8×C17—84no—
42C22×C4×C17—28no—
43C22×C4×C17—28no—
44C22×C4×C17—82no—
45C22×C4×C17—84no—
46C22×C4×C17C22×C418yes—
47C22×C4×C17C22×C414yes—
48C22×C4×C17C2×D414yes—
49C22×C4×C17C2×D414yes—
50C4⋊C4×C17—224no—
51C4⋊C4×C17—84no—
52C22⋊C4×C17—28no—
53C22⋊C4×C17—28no—
54C22⋊C4×C17—216no—
55C22⋊C4×C17—84no—
56C22⋊C4×C17—84no—
57C22⋊C4×C17C22⋊C4116yes—
58C42×C17—84no—
59#21827C1711yesmaximal, characteristic, direct product factor, Sylow
60C23×C17—24no—
61C23×C17—28no—
62C23×C17—44no—
63C23×C17—42no—
64C23×C17—44no—
65C23×C17—44no—
66C23×C17—88no—
67C23×C17C2×C22⋊C414yes—
68C23×C17C23×C411yescharacteristic
69C23×C17C22×D412yes—
70C23×C172−1+414yes—
71Q8×C17—88no—
72C2×C4×C17—28no—
73C2×C4×C17—44no—
74C2×C4×C17—44no—
75C2×C4×C17—44no—
76C2×C4×C17—48no—
77C2×C4×C17—48no—
78C2×C4×C17—48no—
79C2×C4×C17—48no—
80C2×C4×C17—88no—
81C2×C4×C17C2×C22⋊C418yes—
82C2×#543C2×C1711yescharacteristic
83#2312C2×C1712yes—
84#1996C2×C1718yescomplemented
85#1819C2×C1714yes—
86C22×C17—22no—
87C22×C17—22no—
88C22×C17—22no—
89C22×C17—24no—
90C22×C17—28no—
91C22×C17—44no—
92C22×C17—48no—
93C22×C17—88no—
94C22×C17C22×C22⋊C411yescharacteristic
95C22×C17#51912yes—
96C22×C17#53614yes—
97C4×C17—28no—
98C4×C17—48no—
99C4×C17—88no—
100#543—28no—
101C2×C22⋊Q8C4×C1718yescomplemented
102C2×C22⋊Q8C22×C1714yes—
103C22×C22⋊C4C22×C1712yes—
104C22×C22⋊C4C22×C1711yescharacteristic
105#388—28no—
106#380C22×C1714yes—
107#379C22×C1714yes—
108C4×C22⋊C4C22×C1714yes—
109#342C22×C17116yes—
110C2×C17—24no—
111C2×C17—22no—
112C2×C17—44no—
113C2×C17#231011yescharacteristic
114C2×C17#288312yes—
115C25C23×C1711yescharacteristic
116C22×Q8C2×C4×C1714yes—
117C23×C4C2×C4×C1714yes—
118C23×C4C23×C1712yes—
119C22⋊Q8—28no—
120C22⋊Q8—28no—
121C22⋊Q8—232no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4C2×C4×C17112yes—
124C2×C22⋊C4—28no—
125C2×C22⋊C4—24no—
126C2×C22⋊C4—24no—
127C2×C22⋊C4C2×C4×C1714yes—
128C2×C22⋊C4C2×C4×C1714yes—
129C2×C22⋊C4D4×C1718yes—
130C2×C22⋊C4C23×C1718yes—
131C2×C22⋊C4C23×C1714yes—
132C2×C42—24no—
133#95—24no—
134#95—24no—
135C17#2182711yescharacteristic, direct product factor, Sylow
136C24—24no—
137C24—82no—
138C24C22×C4×C1712yes—
139C24C2×D4×C1714yes—
140C24C24×C1711yescharacteristic
141C2×Q8—28no—
142C2×Q8—84no—
143C22×C4—28no—
144C22×C4—28no—
145C22×C4—82no—
146C22×C4—84no—
147C22×C4C22×C4×C1718yes—
148C22×C4C22×C4×C1714yes—
149C22×C4C2×D4×C1714yes—
150C22×C4C2×D4×C1714yes—
151C4⋊C4—224no—
152C4⋊C4—84no—
153C22⋊C4—28no—
154C22⋊C4—28no—
155C22⋊C4—216no—
156C22⋊C4—84no—
157C22⋊C4—84no—
158C22⋊C4C22⋊C4×C17116yes—
159C42—84no—
160C23—24no—
161C23—28no—
162C23—44no—
163C23—42no—
164C23—44no—
165C23—44no—
166C23—88no—
167C23C2×C22⋊C4×C1714yes—
168C23C23×C4×C1711yescharacteristic
169C23C22×D4×C1712yes—
170C23C17×2−1+414yes—
171Q8—88no—
172C2×C4—28no—
173C2×C4—44no—
174C2×C4—44no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—48no—
178C2×C4—48no—
179C2×C4—48no—
180C2×C4—88no—
181C2×C4C2×C22⋊C4×C1718yes—
182C22—22no—
183C22—22no—
184C22—22no—
185C22—24no—
186C22—28no—
187C22—44no—
188C22—48no—
189C22—88no—
190C22C22×C22⋊C4×C1711yescharacteristic
191C22C17×#51912yes—
192C22C17×#53614yes—
193C4—28no—
194C4—48no—
195C4—88no—
196C2—24no—
197C2—22no—
198C2—44no—
199C2C17×#231011yescharacteristic
200C2C17×#288312yes—
subgroupG/H
center, socleC22×C17C22×C22⋊C4
commutatorC23C23×C4×C17
Frattini, cosocleC24C24×C17
prime radicalC25×C17C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C22⋊C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
3. C17×#1996C2semidirect
6. C2×C17×C22⋊Q8C4semidirect
59. #21827C17direct (N × H)
84. #1996C2×C17semidirect
101. C2×C22⋊Q8C4×C17semidirect
135. C17#21827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#5432
C17×#23122
C17×#19962
C17×#18192
#2182717