Finite Group Databasebeta

← #383×#595 #17962965

Subgroups — #383×#595 #17962965

Order 4352.

1566 conjugacy classes of subgroups; only the 424 normal subgroups are shown.

normal subgroups only

This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 424 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×#11763754C211yesmaximal, characteristic
2C2×C42×#595C211yesmaximal, characteristic
3#14543959C216yesmaximal
4#95×#595C216yesmaximal
5D17×#383C211yesmaximal, characteristic
6C22×C4×#595C2214yes—
7C22×C4×#595C2213yes—
8C22×C4×#595C2213yes—
9#11763754C418yescomplemented
10C2×(C2×#595)⋊C4C22112yes—
11C2×(C2×#595)⋊C4C2216yes—
12C42×#595C418yescomplemented
13C2×C42×D17C2211yescharacteristic
14#11762677C411yescharacteristic, complemented
15#11762676C416yescomplemented
16#95×D17C2216yes—
17C17×#383C411yescharacteristic, complemented
18C23×#595C2314yes—
19C23×#595C2313yes—
20C23×#595C2311yescharacteristic
21C22×C4×D17C2314yes—
22C22×C4×D17C2313yes—
23C2×C4×#595—212no—
24C2×C4×#595—212no—
25C2×C4×#595—224no—
26C2×C4×#595C2×C4112yes—
27C2×C4×#595C2×C4112yes—
28C2×C42×C17C2×C411yescharacteristic
29C2×C4×Dic17C2×C413yes—
30C42×D17C2×C414yes—
31C42×D17C2×C414yes—
32(C2×#595)⋊C4—224no—
33(C2×#595)⋊C4C2×C4124yes—
34C17×#95C2×C416yes—
35#10587502C2×C4112yes—
36#10587502C2×C416yes—
37C23×D17C2411yescharacteristic
38C22×#595—26no—
39C22×#595—26no—
40C22×#595—212no—
41C22×#595—212no—
42C22×#595C22×C418yes—
43C22×#595C22×C416yes—
44C22×#595C22×C412yes—
45C22×#595#41112yes—
46C22×#595#41112yes—
47C22×C4×C17C22×C414yes—
48C22×C4×C17C22×C413yes—
49C22×Dic17C22×C414yes—
50C22×Dic17C22×C413yes—
51C2×C4×D17—26no—
52C2×C4×D17—26no—
53C2×C4×D17—212no—
54C2×C4×D17—212no—
55C2×C4×D17C22×C416yes—
56C2×C4×D17C22×C416yes—
57C4×#595—224no—
58C4×#595—224no—
59C4×#595—416no—
60C42×C17C4214yescomplemented
61C4×Dic17C42112yescomplemented
62C4×#383—171nomaximal, Sylow
63C23×C17C23×C411yescharacteristic
64C22×D17C23×C411yescharacteristic
65C22×D17C23×C411yescharacteristic
66C22×D17C2×#4116yes—
67C22×D17C2×#4116yes—
68C2×#595—26no—
69C2×#595—26no—
70C2×#595—224no—
71C2×#595—224no—
72C2×#595—44no—
73C2×#595—412no—
74C2×#595#117112yes—
75C2×#595#117112yes—
76C2×#595#126116yes—
77C2×C4×C17—26no—
78C2×C4×C17—212no—
79C2×C4×C17C2×C4216yes—
80C2×Dic17—26no—
81C2×Dic17—212no—
82C2×Dic17C2×C4216yes—
83C4×D17—26no—
84C4×D17—26no—
85C4×D17—212no—
86C4×D17—44no—
87C4×D17—412no—
88C2×#383—171no—
89C2×#383—171no—
90C2×C43—171no—
91#1434—176no—
92C4×#95—176no—
93C22×C17C22×C4211yescharacteristic
94C22×C17C4×#4116yes—
95C2×D17C2×#11713yes—
96C2×D17C2×#11713yes—
97C2×D17C4×#4116yes—
98C2×D17C2×#12614yes—
99C2×D17#529112yes—
100#595—212no—
101#595—48no—
102#595#38318yesdirect product factor
103C4×C17—26no—
104C4×C17—44no—
105Dic17—26no—
106Dic17—44no—
107C22×C42—171no—
108C22×C42—173no—
109C22×C42—173no—
110C22×C42—174no—
111#383—178no—
112#383—171no—
113#383—176no—
114#383#59511yescharacteristic, direct product factor
115C2×#95—176no—
116C2×#95—176no—
117C2×#95—1712no—
118C43—178no—
119C2×C17C4×#11713yes—
120C2×C17C4×#12614yes—
121D17C2×#38311yescharacteristic
122D17#228313yes—
123D17C4×#12614yes—
124C23×C4—171no—
125C23×C4—173no—
126C23×C4—173no—
127C23×C4—174no—
128C23×C4—174no—
129C2×C42—173no—
130C2×C42—174no—
131C2×C42—174no—
132C2×C42—1712no—
133C2×C42—1712no—
134C2×C42—3412no—
135C2×C42—3412no—
136C2×C42—3424no—
137C2×C42C2×#59511yescharacteristic
138#95—1724no—
139#95—1712no—
140#95—176no—
141#95—3424no—
142#95C2×#59516yes—
143C17C4×#38311yescharacteristic, complemented, Sylow
144C24—171no—
145C22×C4—172no—
146C22×C4—1712no—
147C22×C4—176no—
148C22×C4—1712no—
149C22×C4—173no—
150C22×C4—176no—
151C22×C4—176no—
152C22×C4—178no—
153C22×C4—174no—
154C22×C4—346no—
155C22×C4—346no—
156C22×C4—3412no—
157C22×C4—3412no—
158C22×C4—346no—
159C22×C4—346no—
160C22×C4—3412no—
161C22×C4—3412no—
162C22×C4C22×#59514yes—
163C22×C4C22×#59513yes—
164C42—1712no—
165C42—3424no—
166C42—3424no—
167C42—6816no—
168C42C4×#59514yescomplemented
169C23—171no—
170C23—171no—
171C23—176no—
172C23—176no—
173C23C23×#59511yescharacteristic
174C2×C4—26no—
175C2×C4—212no—
176C2×C4—1712no—
177C2×C4—1716no—
178C2×C4—1712no—
179C2×C4—176no—
180C2×C4—346no—
181C2×C4—346no—
182C2×C4—3412no—
183C2×C4—346no—
184C2×C4—346no—
185C2×C4—3424no—
186C2×C4—346no—
187C2×C4—3424no—
188C2×C4—3412no—
189C2×C4—684no—
190C2×C4—6812no—
191C2×C4—684no—
192C2×C4—6812no—
193C2×C4C2×C4×#59516yes—
194C22—173no—
195C22—173no—
196C22—176no—
197C22—174no—
198C22—1712no—
199C22C22×C4×#59511yescharacteristic
200C22#41×#59516yes—
201C4—26no—
202C4—44no—
203C4—178no—
204C4—3412no—
205C4—346no—
206C4—688no—
207C4—684no—
208C2—171no—
209C2—173no—
210C2—174no—
211C2#117×#59513yes—
212C2#126×#59514yes—
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#383C4
socleC23×C17C23×C4
prime radical, cosocleC23×D17C24
hypercenter#383#595
hypocenterC17C4×#383
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
9. #11763754C4semidirect
12. C42×#595C4semidirect
14. #11762677C4semidirect
15. #11762676C4semidirect
17. C17×#383C4semidirect
60. C42×C17C42semidirect
61. C4×Dic17C42semidirect
102. #595#383direct (N × H)
114. #383#595direct (N × H)
143. C17C4×#383semidirect
168. C42C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637542
C2×C42×#5952
#145439592
#95×#5952
D17×#3832
C4×#38317