Finite Group Databasebeta

← #17033434

Subgroups — #17033434

Order 4352.

5990 conjugacy classes of subgroups; only the 699 normal subgroups are shown.

normal subgroups only

This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 699 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×#11762773C216yesmaximal, complemented
2#14528694C218yesmaximal, complemented
3C25×C4×C17C211yesmaximal, characteristic
4C22×#63223C2214yescomplemented
5#11762773—224no—
6C2×C22⋊#3622C22124yescomplemented
7C26×C17C411yescharacteristic
8C24×C4×C17—224no—
9C24×C4×C17C413yes—
10C24×C4×C17C414yes—
11C24×C4×C17C2214yes—
12C24×C4×C17C2213yes—
13C25×C17—212no—
14C25×C17—216no—
15C25×C17C2×C413yes—
16C25×C17C2×C414yes—
17C23×C4×C17—2128no—
18C23×C4×C17—212no—
19C23×C4×C17—224no—
20C23×C4×C17—248no—
21C23×C4×C17—248no—
22C23×C4×C17—224no—
23C23×C4×C17C2×C4112yes—
24C23×C4×C17C2×C413yes—
25C23×C4×C17C2×C416yes—
26C23×C4×C17D4124yes—
27C23×C4×C17C2316yes—
28C23×C4×C17C2311yescharacteristic
29C2×#63223—224no—
30C22×#3622C2318yescomplemented
31C22⋊#3622—248no—
32C24×C17—232no—
33C24×C17—2192no—
34C24×C17—224no—
35C24×C17—212no—
36C24×C17—224no—
37C24×C17—224no—
38C24×C17C22⋊C4112yes—
39C24×C17M16116yescomplemented
40C24×C17C22×C411yescharacteristic
41C24×C17C22×C416yes—
42C22×C4×C17—296no—
43C22×C4×C17—2128no—
44C22×C4×C17—2128no—
45C22×C4×C17—224no—
46C22×C4×C17—212no—
47C22×C4×C17—248no—
48C22×C4×C17—224no—
49C22×C4×C17—296no—
50C22×C4×C17—224no—
51C22×C4×C17C22⋊C4112yes—
52C22×C4×C17C22⋊C4124yes—
53C22×C4×C17C22×C416yes—
54C22×C4×C17C22×C411yescharacteristic
55C22×C4×C17C2×D4124yes—
56C22×C4×C17C2×D4112yes—
57C22×C4×C17C2411yescharacteristic
58#63223—416no—
59C2×#3622—224no—
60#20579—171nomaximal, Sylow
61C23×C17—232no—
62C23×C17—2256no—
63C23×C17—296no—
64C23×C17—296no—
65C23×C17—212no—
66C23×C17—24no—
67C23×C17—212no—
68C23×C17—224no—
69C23×C17—248no—
70C23×C17—296no—
71C23×C17C2×C22⋊C416yes—
72C23×C17C2×C22⋊C4112yes—
73C23×C17C2×M16124yes—
74C23×C17C23×C411yescharacteristic
75C2×C4×C17—296no—
76C2×C4×C17—212no—
77C2×C4×C17—224no—
78C2×C4×C17—248no—
79C2×C4×C17—248no—
80C2×C4×C17C2×C22⋊C4112yes—
81C2×C4×C17C2×C22⋊C416yes—
82C2×C4×C17#120116yes—
83C2×C4×C17C22×D416yes—
84#3622—48no—
85C25×C4D1711yescharacteristic
86C2×#407—176no—
87#1779—178no—
88C22×C17—296no—
89C22×C17—2128no—
90C22×C17—212no—
91C22×C17—212no—
92C22×C17—248no—
93C22×C17—212no—
94C22×C17#37914yes—
95C22×C17#407124yescomplemented
96C22×C17C22×C22⋊C413yes—
97C22×C17C22×M1614yes—
98C4×C17—212no—
99C4×C17#37914yes—
100C4×C17C2×#12014yes—
101C26Dic1711yescharacteristic
102C24×C4—224no—
103C24×C4Dic1713yes—
104C24×C4Dic1714yes—
105C24×C4C2×D1714yes—
106C24×C4C2×D1713yes—
107C22×M16—174no—
108#407—3424no—
109C2×C22⋊C8—1724no—
110C2×C17—24no—
111C2×C17—224no—
112C2×C17C2×#37911yescharacteristic
113C2×C17C2×#40716yes—
114C25—212no—
115C25—216no—
116C25C2×Dic1713yes—
117C25C2×Dic1714yes—
118C23×C4—2128no—
119C23×C4—212no—
120C23×C4—224no—
121C23×C4—248no—
122C23×C4—248no—
123C23×C4—224no—
124C23×C4C2×Dic17112yes—
125C23×C4C2×Dic1713yes—
126C23×C4C2×Dic1716yes—
127C23×C4C22⋊D17124yes—
128C23×C4C22×D1716yes—
129C23×C4C22×D1711yescharacteristic
130C2×M16—3424no—
131C22×C8—178no—
132C22⋊C8—3448no—
133C17#2057911yescharacteristic, complemented, Sylow
134C24—232no—
135C24—2192no—
136C24—224no—
137C24—224no—
138C24—224no—
139C24—212no—
140C24#63223116yescomplemented
141C24C22⋊Dic17112yes—
142C24C22×Dic1716yes—
143C24C22×Dic1711yescharacteristic
144C22×C4—296no—
145C22×C4—2128no—
146C22×C4—2128no—
147C22×C4—224no—
148C22×C4—212no—
149C22×C4—224no—
150C22×C4—248no—
151C22×C4—224no—
152C22×C4—296no—
153C22×C4C22⋊Dic17112yes—
154C22×C4C22⋊Dic17124yes—
155C22×C4C22×Dic1716yes—
156C22×C4C22×Dic1711yescharacteristic
157C22×C4C2×C22⋊D17124yes—
158C22×C4C2×C22⋊D17112yes—
159C22×C4C23×D1711yescharacteristic
160M16—6816no—
161C2×C8—3424no—
162C23—232no—
163C23—2256no—
164C23—296no—
165C23—296no—
166C23—212no—
167C23—248no—
168C23—296no—
169C23—212no—
170C23—24no—
171C23—224no—
172C23C2×#63223124yes—
173C23C2×C22⋊Dic17112yes—
174C23C2×C22⋊Dic1716yes—
175C23C23×Dic1711yescharacteristic
176C2×C4—296no—
177C2×C4—212no—
178C2×C4—224no—
179C2×C4—248no—
180C2×C4—248no—
181C2×C4C2×C22⋊Dic17112yes—
182C2×C4C2×C22⋊Dic1716yes—
183C2×C4#10587639116yes—
184C2×C4C22×C22⋊D1716yes—
185C8—688no—
186C22—2128no—
187C22—296no—
188C22—248no—
189C22—212no—
190C22—212no—
191C22—212no—
192C22#1176266514yes—
193C22#11762773124yescomplemented
194C22C22×C22⋊Dic1713yes—
195C22C22×#6322314yes—
196C4—212no—
197C4#1176266514yes—
198C4C2×#1058763914yes—
199C2—224no—
200C2—24no—
201C2C2×#1176266511yescharacteristic
202C2C2×#1176277316yes—
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC25×C4×C17C2
prime radicalC26×C17C4
cosocleC22×C4×C17C24
hypercenterC25×C4D17
hypocenterC17#20579
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C25×C4

Complements

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

NH ≅ G/Ntype
1. C2×#11762773C2semidirect
2. #14528694C2semidirect
4. C22×#63223C22semidirect
6. C2×C22⋊#3622C22semidirect
30. C22×#3622C23semidirect
39. C24×C17M16semidirect
95. C22×C17#407semidirect
133. C17#20579semidirect
140. C24#63223semidirect
193. C22#11762773semidirect

Maximal subgroups

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

subgroupindex
C2×#117627732
#145286942
C25×C4×C172
#2057917