Finite Group Databasebeta

← #17963107

Subgroups — #17963107

Order 4352.

1774 conjugacy classes of subgroups; only the 432 normal subgroups are shown.

normal subgroups only

This group has 1774 conjugacy classes of subgroups — too many to draw. Only its 432 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×C4×C4⋊#595C216yesmaximal
2#14543972C218yesmaximal
3D17×#376C211yesmaximal, characteristic
4C22×C4⋊#595C22112yes—
5C22×C4×#595C2214yes—
6C4×C4⋊#595—224no—
7C2×(C2×#595)⋊C4C22112yes—
8C2×C42×D17C2213yes—
9#11762655C413yescomplemented
10#11762654C414yescomplemented
11#95×D17C2214yes—
12C17×#376C411yescharacteristic, complemented
13C23×#595C2318yes—
14C22×C4×D17C2316yes—
15C22×C4×D17C2311yescharacteristic
16C2×C4⋊#595—248no—
17C2×C4⋊#595—224no—
18C2×C4×#595—224no—
19C2×C42×C17C2×C413yes—
20C2×C4×Dic17C2×C416yes—
21C2×C4×Dic17C2×C413yes—
22C42×D17D4112yes—
23C42×D17Q8112yes—
24(C2×#595)⋊C4—224no—
25C17×#95C2×C414yes—
26#10587502C2×C4112yes—
27C23×D17C2411yescharacteristic
28C22×#595—224no—
29C22×#595—224no—
30C22×#595#41116yes—
31C22×C4×C17C22×C416yes—
32C22×C4×C17C22×C411yescharacteristic
33C22×Dic17C22×C416yes—
34C22×Dic17C22×C411yescharacteristic
35C2×C4×D17—224no—
36C2×C4×D17C2×D4112yes—
37C2×C4×D17C2×D416yes—
38C2×C4×D17C2×Q8112yes—
39C2×C4×D17C2×Q816yes—
40C4⋊#595—296no—
41C4×#595—416no—
42C42×C17C4⋊C4112yescomplemented
43C4×Dic17C4⋊C4112yescomplemented
44C4×Dic17C4⋊C4124yescomplemented
45#13856—171nomaximal, Sylow
46C23×C17C23×C411yescharacteristic
47C22×D17C22×D413yes—
48C22×D17C22×Q813yes—
49C22×D17C2×#4118yes—
50C2×#595—248no—
51C2×#595—424no—
52C2×#595—48no—
53C2×C4×C17—212no—
54C2×C4×C17C2×C4⋊C4112yes—
55C2×C4×C17C2×C4⋊C416yes—
56C2×Dic17—212no—
57C2×Dic17C2×C4⋊C4112yes—
58C2×Dic17C2×C4⋊C416yes—
59C4×D17—224no—
60C4×D17—224no—
61C4×D17#12714yes—
62C4×D17C4⋊Q8112yes—
63C2×C4×C4⋊C4—176no—
64C2×#376—171no—
65#1444—178no—
66C22×C17C22×C4⋊C413yes—
67C22×C17C4×#4114yes—
68C2×D17#525112yes—
69C2×D17C2×#12711yescharacteristic
70C2×D17C2×C4⋊Q813yes—
71C2×D17#533112yes—
72#595—416no—
73C4×C17—212no—
74C4×C17#38414yes—
75Dic17—212no—
76Dic17#38414yes—
77C22×C4⋊C4—1712no—
78C22×C42—173no—
79C22×C42—174no—
80C4×C4⋊C4—3424no—
81#376—173no—
82#376—174no—
83#376#59511yescharacteristic, complemented
84C2×#95—174no—
85C2×#95—1712no—
86C2×C17C2×#38411yescharacteristic
87C2×C17#229616yes—
88D17#239712yes—
89D17#239916yes—
90C23×C4—171no—
91C23×C4—176no—
92C23×C4—178no—
93C2×C4⋊C4—3448no—
94C2×C4⋊C4—3424no—
95C2×C42—176no—
96C2×C42—173no—
97C2×C42—1712no—
98C2×C42—1712no—
99C2×C42—3424no—
100C2×C42C2×#59513yes—
101#95—1712no—
102#95—3424no—
103#95C2×#59514yes—
104C17#1385611yescharacteristic, complemented, Sylow
105C24—171no—
106C22×C4—171no—
107C22×C4—176no—
108C22×C4—176no—
109C22×C4—176no—
110C22×C4—1712no—
111C22×C4—1712no—
112C22×C4—1716no—
113C22×C4—3424no—
114C22×C4—3424no—
115C22×C4—3424no—
116C22×C4C22×#59516yes—
117C22×C4C22×#59511yescharacteristic
118C4⋊C4—3496no—
119C42—1724no—
120C42—1712no—
121C42—6816no—
122C42C4⋊#595112yescomplemented
123C23—173no—
124C23—173no—
125C23—178no—
126C23C23×#59511yescharacteristic
127C2×C4—212no—
128C2×C4—176no—
129C2×C4—174no—
130C2×C4—1712no—
131C2×C4—1712no—
132C2×C4—3424no—
133C2×C4—3424no—
134C2×C4—3412no—
135C2×C4—3448no—
136C2×C4—688no—
137C2×C4—6824no—
138C2×C4C2×C4⋊#595112yes—
139C2×C4C2×C4⋊#59516yes—
140C22—171no—
141C22—173no—
142C22—1712no—
143C22—1712no—
144C22C22×C4⋊#59513yes—
145C22#41×#59514yes—
146C4—212no—
147C4—174no—
148C4—3412no—
149C4—6816no—
150C4#1176375514yes—
151C2—172no—
152C2—176no—
153C2C2×#1176375511yescharacteristic
154C2#1454524416yes—
subgroupG/H
centerC22×C4C22×#595
commutator, socleC23×C17C23×C4
FrattiniC23C23×#595
FittingC17×#376C4
prime radical, cosocleC23×D17C24
hypercenter#376#595
hypocenterC17#13856
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #376

Complements

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

NH ≅ G/Ntype
9. #11762655C4semidirect
10. #11762654C4semidirect
12. C17×#376C4semidirect
42. C42×C17C4⋊C4semidirect
43. C4×Dic17C4⋊C4semidirect
44. C4×Dic17C4⋊C4semidirect
83. #376#595semidirect
104. C17#13856semidirect
122. C42C4⋊#595semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊#5952
#145439722
D17×#3762
#1385617