Finite Group Databasebeta

← C17×#10936 #16868680

Subgroups — C17×#10936 #16868680

Order 4352.

1258 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 302 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×#381C213yesmaximal
2C17×#2273C211yesmaximal, characteristic
3C2×C17×#342C213yesmaximal
4C24×C4×C17C2211yescharacteristic
5C22×C22⋊C4×C17C2213yes—
6C22×C22⋊C4×C17C2213yes—
7C17×#381—26no—
8C17×#381C4112yescomplemented
9C4×C22⋊C4×C17—26no—
10C2×C17×#95—26no—
11C17×#342—26no—
12C25×C17C2311yescharacteristic
13C23×C4×C17—23no—
14C23×C4×C17—23no—
15C23×C4×C17—26no—
16C23×C4×C17—23no—
17C23×C4×C17C2×C416yes—
18C23×C4×C17D416yes—
19C2×C22⋊C4×C17—26no—
20C2×C22⋊C4×C17—26no—
21C2×C22⋊C4×C17—26no—
22C2×C22⋊C4×C17—26no—
23C2×C22⋊C4×C17—23no—
24C2×C22⋊C4×C17C2×C416yes—
25C2×C22⋊C4×C17C2×C416yes—
26C2×C22⋊C4×C17D416yes—
27C2×C42×C17—24no—
28C17×#95—24no—
29C17×#95—224no—
30C24×C17—44no—
31C24×C17C22×C413yes—
32C24×C17C2×D413yes—
33C24×C17C2×D413yes—
34C24×C17#4116yes—
35C22×C4×C17—26no—
36C22×C4×C17—26no—
37C22×C4×C17—212no—
38C22×C4×C17—212no—
39C22×C4×C17—26no—
40C22×C4×C17—26no—
41C22×C4×C17—26no—
42C22×C4×C17—41no—
43C22×C4×C17—46no—
44C22×C4×C17—43no—
45C22×C4×C17—43no—
46C22×C4×C17—42no—
47C22×C4×C17—41no—
48C22×C4×C17—412no—
49C22×C4×C17—412no—
50C22×C4×C17—46no—
51C22×C4×C17C4214yescomplemented
52C22×C4×C17C22⋊C4112yes—
53C22⋊C4×C17—212no—
54C22⋊C4×C17—212no—
55C22⋊C4×C17—212no—
56C22⋊C4×C17—43no—
57C22⋊C4×C17—43no—
58C42×C17—84no—
59#10936C1711yesmaximal, characteristic, direct product factor, Sylow
60C23×C17—212no—
61C23×C17—46no—
62C23×C17—46no—
63C23×C17—412no—
64C23×C17C2×C4211yescharacteristic
65C23×C17C2×C22⋊C413yes—
66C23×C17#11713yes—
67C23×C17C4×D416yes—
68C23×C17C4×D416yes—
69C23×C17#12011yescharacteristic
70C23×C17#12116yes—
71C23×C17#12313yes—
72C23×C17#12413yes—
73C23×C17#12612yes—
74C23×C17#12711yescharacteristic
75C2×C4×C17—212no—
76C2×C4×C17—212no—
77C2×C4×C17—46no—
78C2×C4×C17—412no—
79C2×C4×C17—46no—
80C2×C4×C17—412no—
81C2×C4×C17—412no—
82C2×C4×C17—412no—
83C2×C4×C17—46no—
84C2×C4×C17—86no—
85C2×C4×C17—812no—
86C2×#381C2×C1713yes—
87#2273C2×C1711yescharacteristic
88C2×#342C2×C1713yes—
89C22×C17—26no—
90C22×C17—212no—
91C22×C17—26no—
92C22×C17—212no—
93C22×C17—41no—
94C22×C17—43no—
95C22×C17—46no—
96C22×C17—43no—
97C22×C17—42no—
98C22×C17—41no—
99C22×C17C4×C22⋊C413yes—
100C22×C17#38613yes—
101C22×C17#38816yes—
102C22×C17#39013yes—
103C22×C17#45814yes—
104C4×C17—412no—
105C4×C17—44no—
106C4×C17—86no—
107C24×C4C22×C1711yescharacteristic
108C22×C22⋊C4C22×C1713yes—
109C22×C22⋊C4C22×C1713yes—
110#381—26no—
111#381C4×C17112yescomplemented
112C4×C22⋊C4—26no—
113C2×#95—26no—
114#342—26no—
115C2×C17—23no—
116C2×C17—23no—
117C2×C17—26no—
118C2×C17#143711yescharacteristic
119C2×C17#189016yes—
120C25C23×C1711yescharacteristic
121C23×C4—23no—
122C23×C4—23no—
123C23×C4—26no—
124C23×C4—23no—
125C23×C4C2×C4×C1716yes—
126C23×C4D4×C1716yes—
127C2×C22⋊C4—26no—
128C2×C22⋊C4—26no—
129C2×C22⋊C4—26no—
130C2×C22⋊C4—26no—
131C2×C22⋊C4—23no—
132C2×C22⋊C4C2×C4×C1716yes—
133C2×C22⋊C4C2×C4×C1716yes—
134C2×C22⋊C4D4×C1716yes—
135C2×C42—24no—
136#95—24no—
137#95—224no—
138C17#1093611yescharacteristic, direct product factor, Sylow
139C24—44no—
140C24C22×C4×C1713yes—
141C24C2×D4×C1713yes—
142C24C2×D4×C1713yes—
143C24#41×C1716yes—
144C22×C4—26no—
145C22×C4—26no—
146C22×C4—212no—
147C22×C4—212no—
148C22×C4—26no—
149C22×C4—26no—
150C22×C4—26no—
151C22×C4—43no—
152C22×C4—43no—
153C22×C4—42no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—46no—
157C22×C4—412no—
158C22×C4—412no—
159C22×C4—46no—
160C22×C4C42×C1714yescomplemented
161C22×C4C22⋊C4×C17112yes—
162C22⋊C4—212no—
163C22⋊C4—212no—
164C22⋊C4—212no—
165C22⋊C4—43no—
166C22⋊C4—43no—
167C42—84no—
168C23—212no—
169C23—46no—
170C23—46no—
171C23—412no—
172C23C2×C42×C1711yescharacteristic
173C23C2×C22⋊C4×C1713yes—
174C23C17×#11713yes—
175C23C4×D4×C1716yes—
176C23C4×D4×C1716yes—
177C23C17×#12011yescharacteristic
178C23C17×#12116yes—
179C23C17×#12313yes—
180C23C17×#12413yes—
181C23C17×#12612yes—
182C23C17×#12711yescharacteristic
183C2×C4—212no—
184C2×C4—212no—
185C2×C4—46no—
186C2×C4—412no—
187C2×C4—46no—
188C2×C4—412no—
189C2×C4—412no—
190C2×C4—412no—
191C2×C4—46no—
192C2×C4—86no—
193C2×C4—812no—
194C22—26no—
195C22—26no—
196C22—212no—
197C22—212no—
198C22—43no—
199C22—42no—
200C22—41no—
201C22—41no—
202C22—43no—
203C22—46no—
204C22C4×C22⋊C4×C1713yes—
205C22C17×#38613yes—
206C22C17×#38816yes—
207C22C17×#39013yes—
208C22C17×#45814yes—
209C4—44no—
210C4—412no—
211C4—86no—
212C2—23no—
213C2—23no—
214C2—26no—
215C2C17×#143711yescharacteristic
216C2C17×#189016yes—
subgroupG/H
center, socleC23×C17#120
commutatorC23C2×C42×C17
Frattini, cosocleC25C23×C17
prime radicalC25×C17C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C17 ◁ C25×C17 ◁ G

Complements

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

NH ≅ G/Ntype
8. C17×#381C4semidirect
51. C22×C4×C17C42semidirect
59. #10936C17direct (N × H)
111. #381C4×C17semidirect
138. C17#10936direct (N × H)
160. C22×C4C42×C17semidirect

Maximal subgroups

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

subgroupindex
C2×C17×#3812
C17×#22732
C2×C17×#3422
#1093617