Finite Group Databasebeta

← D17×#2845 #17240911

Subgroups — D17×#2845 #17240911

Order 4352.

1742 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 579 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
1#14537059C213yesmaximal, complemented
2#14537058C2112yesmaximal, complemented
3D17×#398C2112yesmaximal
4D17×#382C213yesmaximal
5C17×#2845C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D17C2216yes—
7C2×C4⋊C4×D17C22112yes—
8C2×C42×D17C2211yescharacteristic
9#11762743C22112yes—
10#11762743C22112yes—
11#11762742C22112yes—
12#11762742C22112yes—
13#11762741C22112yes—
14#11762740C22112yes—
15#11762739C22112yes—
16#11762675C2213yes—
17#11762674C2216yes—
18#11762673C22112yes—
19#95×D17C22112yes—
20#95×D17C2214yes—
21C17×#398C22112yes—
22C17×#382C2213yes—
23C22×C4×D17C23112yes—
24C22×C4×D17C2313yes—
25C2×C4⋊C4×C17C23112yes—
26C2×C4⋊C4×C17C2316yes—
27C2×C42×C17C2311yescharacteristic
28C2×C4⋊Dic17C23112yes—
29C2×C4⋊Dic17C2316yes—
30C2×#63225C23112yes—
31C2×#63225C23112yes—
32C2×#63225C23112yes—
33C2×C4×Dic17C2313yes—
34C4⋊C4×D17—412no—
35C4⋊C4×D17—424no—
36C42×D17Q818yes—
37C17×#95C23112yes—
38C17×#95C2314yes—
39#10587502C23112yes—
40#10587502C23112yes—
41#10587502C23112yes—
42#10587502C23112yes—
43C23×D17C2411yescharacteristic
44C22×C4×C17C24112yes—
45C22×C4×C17C2413yes—
46C22×Dic17C24112yes—
47C22×Dic17C2413yes—
48C2×C4×D17—26no—
49C2×C4×D17—26no—
50C2×C4×D17—224no—
51C2×C4×D17—224no—
52C2×C4×D17—224no—
53C2×C4×D17C2×Q8112yes—
54C4⋊C4×C17—46no—
55C4⋊C4×C17—412no—
56C42×C17C2×Q814yes—
57C4⋊Dic17—412no—
58C4⋊Dic17—46no—
59#63225—412no—
60#63225—412no—
61#63225—412no—
62C4×Dic17C2×Q8112yes—
63C2×#2845—171nomaximal, Sylow
64C23×C17C2511yescharacteristic
65C22×D17C22×Q812yes—
66C22×D17H(5,𝔽2)16yes—
67C22×D172−1+416yes—
68C2×C4×C17—23no—
69C2×C4×C17—23no—
70C2×C4×C17—212no—
71C2×C4×C17—212no—
72C2×C4×C17—212no—
73C2×C4×C17C22×Q816yes—
74C2×Dic17—23no—
75C2×Dic17—23no—
76C2×Dic17—212no—
77C2×Dic17—212no—
78C2×Dic17—212no—
79C2×Dic17C22×Q816yes—
80C4×D17—224no—
81C4×D17—448no—
82#2845—1712no—
83#2845—173no—
84#2845D1711yescharacteristic, direct product factor
85C2×#398—1712no—
86C2×#382—173no—
87C22×C17C23×Q811yescharacteristic
88C22×C17C2×H(5,𝔽2)13yes—
89C22×C17C2×2−1+413yes—
90C2×D17#544112yes—
91C2×D17#562112yes—
92C2×D17#56414yes—
93C4×C17—26no—
94C4×C17—412no—
95Dic17—26no—
96Dic17—412no—
97C22×C4⋊C4—1712no—
98C22×C4⋊C4—176no—
99C22×C42—171no—
100#398—1712no—
101#398—1712no—
102#398—1712no—
103#398—1712no—
104#398—1712no—
105#398—1712no—
106#398—1712no—
107#398C2×D17112yes—
108#382—176no—
109#382—173no—
110#382—1712no—
111#382C2×D1713yes—
112C2×#95—174no—
113C2×#95—1712no—
114C2×C17C2×#54413yes—
115C2×C17C2×#56213yes—
116C2×C17C2×#56411yescharacteristic
117D17#284518yesdirect product factor
118C23×C4—173no—
119C23×C4—1712no—
120C2×C4⋊C4—1712no—
121C2×C4⋊C4—176no—
122C2×C4⋊C4—1712no—
123C2×C4⋊C4—1712no—
124C2×C4⋊C4—1712no—
125C2×C4⋊C4—6812no—
126C2×C4⋊C4—6824no—
127C2×C4⋊C4C22×D1716yes—
128C2×C4⋊C4C22×D17112yes—
129C2×C42—173no—
130C2×C42—178no—
131C2×C42C22×D1711yescharacteristic
132#95—1712no—
133#95—1712no—
134#95—1712no—
135#95—1712no—
136#95C22×D17112yes—
137#95C22×D1714yes—
138C17C2×#284511yescharacteristic, complemented, Sylow
139C24—171no—
140C22×C4—173no—
141C22×C4—1712no—
142C22×C4—1712no—
143C22×C4—346no—
144C22×C4—346no—
145C22×C4—3424no—
146C22×C4—3424no—
147C22×C4—3424no—
148C22×C4C23×D17112yes—
149C22×C4C23×D1713yes—
150C4⋊C4—46no—
151C4⋊C4—412no—
152C4⋊C4—6812no—
153C4⋊C4—6812no—
154C4⋊C4—6812no—
155C4⋊C4—686no—
156C4⋊C4—6812no—
157C42—1712no—
158C42Q8×D1714yes—
159C23—172no—
160C23—176no—
161C23—176no—
162C23C24×D1711yescharacteristic
163C2×C4—23no—
164C2×C4—23no—
165C2×C4—212no—
166C2×C4—212no—
167C2×C4—212no—
168C2×C4—176no—
169C2×C4—3424no—
170C2×C4—343no—
171C2×C4—343no—
172C2×C4—3412no—
173C2×C4—3412no—
174C2×C4—3412no—
175C2×C4—6848no—
176C2×C4C2×Q8×D1716yes—
177C22—1712no—
178C22—174no—
179C22—1712no—
180C22C22×Q8×D1711yescharacteristic
181C22H(5,𝔽2)×D1713yes—
182C222−1+4×D1713yes—
183C4—26no—
184C4—412no—
185C4—346no—
186C4—6812no—
187C2—178no—
188C2D17×#54413yes—
189C2D17×#56213yes—
190C2D17×#56411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2845C2
prime radicalC23×D17C24
hypercenter#2845D17
hypocenterC17C2×#2845
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2845

Complements

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

NH ≅ G/Ntype
1. #14537059C2semidirect
2. #14537058C2semidirect
5. C17×#2845C2semidirect
84. #2845D17direct (N × H)
117. D17#2845direct (N × H)
138. C17C2×#2845semidirect

Maximal subgroups

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

subgroupindex
#145370592
#145370582
D17×#3982
D17×#3822
C17×#28452
C2×#284517