Finite Group Databasebeta

← #16943760

Subgroups — #16943760

Order 4352.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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#14530596C212yesmaximal, complemented
2#14526735C212yesmaximal, complemented
3#14526720C212yesmaximal
4C17×#2921C211yesmaximal, characteristic
5#11762630—22no—
6#11762591C2214yes—
7#11762587—22no—
8C2×C17×#117C411yescharacteristic
9C17×#433—22no—
10C17×#433—22no—
11C17×#423C411yescharacteristic
12C17×#423C2211yescharacteristic
13C17×#407C411yescharacteristic
14C17×#407C2211yescharacteristic
15C4×M16×C17C411yescharacteristic
16C4×M16×C17C2211yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C2×M16×C17C2×C411yescharacteristic
19C2×M16×C17C2×C411yescharacteristic
20C2×M16×C17C2×C411yescharacteristic
21C2×M16×C17C2311yescharacteristic
22C17×#117—21no—
23C17×#117—21no—
24C17×#117—22no—
25C2×C4⋊C4×C17—21no—
26C2×C22⋊C4×C17—21no—
27C2×C42×C17C2×C411yescharacteristic
28C2×C42×C17C2×C411yescharacteristic
29C17×C4⋊C8—22no—
30C17×C4⋊C8—22no—
31C17×C22⋊C8—22no—
32C17×C22⋊C8—22no—
33C17×#97—21no—
34C17×#97D412yes—
35C4×C8×C17—21no—
36C4×C8×C17D412yes—
37#10587483—24no—
38C24×C17M1611yescharacteristic
39C22×C4×C17—21no—
40C22×C4×C17—21no—
41C22×C4×C17—21no—
42C22×C4×C17—21no—
43C22×C4×C17—41no—
44C22×C4×C17—41no—
45C22×C4×C17M1611yescharacteristic
46C22×C4×C17C22×C411yescharacteristic
47M16×C17—41no—
48M16×C17—41no—
49M16×C17—41no—
50M16×C17—41no—
51C2×C8×C17—21no—
52C2×C8×C17—21no—
53C2×C8×C17C22⋊C412yes—
54C2×C8×C17C2×D412yes—
55C4⋊C4×C17—22no—
56C4⋊C4×C17—22no—
57C22⋊C4×C17—22no—
58C22⋊C4×C17—22no—
59C42×C17—21no—
60C42×C17—21no—
61C42×C17C22⋊C411yescharacteristic
62C42×C17C22⋊C411yescharacteristic
63C42×C17M1612yes—
64#63214—44no—
65#11522—171nomaximal, Sylow
66C23×C17—21no—
67C23×C17—41no—
68C23×C17—81no—
69C23×C17C2×M1611yescharacteristic
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—22no—
75C2×C4×C17—21no—
76C2×C4×C17—42no—
77C2×C4×C17—41no—
78C2×C4×C17—41no—
79C2×C4×C17—41no—
80C2×C4×C17—81no—
81C2×C4×C17—81no—
82C2×C4×C17C2×C22⋊C411yescharacteristic
83C2×C4×C17C2×M1611yescharacteristic
84C8×C17—22no—
85C8×C17—22no—
86C8×C17—41no—
87C8×C17—41no—
88#2921D1711yescharacteristic
89#2165—172no—
90#1327—172no—
91#1320—172no—
92C22×C17—21no—
93C22×C17—41no—
94C22×C17—42no—
95C22×C17—41no—
96C22×C17—82no—
97C22×C17#40711yescharacteristic
98C4×C17—21no—
99C4×C17—41no—
100C4×C17—41no—
101C4×C17—42no—
102C4×C17—41no—
103C4×C17#41011yescharacteristic
104C4×C17#41311yescharacteristic
105C2×#117Dic1711yescharacteristic
106#433—22no—
107#433—22no—
108#423Dic1711yescharacteristic
109#423C2×D1711yescharacteristic
110#407Dic1711yescharacteristic
111#407C2×D1711yescharacteristic
112C4×M16Dic1711yescharacteristic
113C4×M16C2×D1711yescharacteristic
114#364—342no—
115#349—174no—
116#347—342no—
117C2×C17—21no—
118C2×C17—41no—
119C2×C17—81no—
120C2×C17#146411yescharacteristic
121C23×C4C2×Dic1711yescharacteristic
122C2×M16C2×Dic1711yescharacteristic
123C2×M16C2×Dic1711yescharacteristic
124C2×M16C2×Dic1711yescharacteristic
125C2×M16C22×D1711yescharacteristic
126#117—21no—
127#117—21no—
128#117—22no—
129C2×C4⋊C4—21no—
130C2×C22⋊C4—21no—
131C2×C42C2×Dic1711yescharacteristic
132C2×C42C2×Dic1711yescharacteristic
133M32—344no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C22⋊C8—22no—
137C22⋊C8—22no—
138#97—21no—
139#97C22⋊D1712yes—
140C4×C8—21no—
141C4×C8C22⋊D1712yes—
142C17#1152211yescharacteristic, complemented, Sylow
143C24#6322311yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4#6322311yescharacteristic
151C22×C4C22×Dic1711yescharacteristic
152M16—41no—
153M16—41no—
154M16—41no—
155M16—41no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8C22⋊Dic1712yes—
159C2×C8C2×C22⋊D1712yes—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C42—21no—
165C42—21no—
166C42#6322312yes—
167C42C22⋊Dic1711yescharacteristic
168C42C22⋊Dic1711yescharacteristic
169C16—684no—
170C23—21no—
171C23—41no—
172C23—81no—
173C23C2×#6322311yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4C2×#6322311yescharacteristic
187C2×C4C2×C22⋊Dic1711yescharacteristic
188C8—22no—
189C8—22no—
190C8—41no—
191C8—41no—
192C22—21no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—82no—
197C22#1176277311yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—42no—
202C4—41no—
203C4#1176278311yescharacteristic
204C4#1176279311yescharacteristic
205C2—21no—
206C2—41no—
207C2—81no—
208C2#1452711811yescharacteristic
subgroupG/H
centerC4#11762783
commutatorC22×C4×C17C22×C4
FrattiniC2×M16C22×D17
FittingC17×#2921C2
socleC2×C17#1464
prime radicalC24×C17M16
cosocleC2×M16×C17C23
hypercenter#2921D17
hypocenterC17#11522
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C42 ◁ C4×M16 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. #14530596C2semidirect
2. #14526735C2semidirect
142. C17#11522semidirect

Maximal subgroups

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

subgroupindex
#145305962
#145267352
#145267202
C17×#29212
#1152217