Finite Group Databasebeta

← #11928702

Subgroups — #11928702

Order 1248.

188 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 50 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×#64625C211yesmaximal, characteristic, complemented
2C2×C3×C22⋊D13C211yesmaximal, characteristic, complemented
3C2×#64603C211yesmaximal, characteristic, complemented
4C2×Dic3×D13C211yesmaximal, characteristic, complemented
5C13×#217C211yesmaximal, characteristic, complemented
6#10597612C211yesmaximal, characteristic, complemented
7#10597610C211yesmaximal, characteristic, complemented
8#88138—31nomaximal, Hall
9C23×C3×C13C2211yescharacteristic
10C22×D39C2211yescharacteristic
11C22×C3×D13C2211yescharacteristic
12#64625—22no—
13C2×Dic39C2211yescharacteristic
14C2×Dic3×C13C2211yescharacteristic
15C2×Dic3×C13C2211yescharacteristic
16C3×C22⋊D13—22no—
17C2×C3×Dic13C2211yescharacteristic
18#64603—22no—
19Dic3×D13—22no—
20C2×C22⋊D13—31no—
21C2×C22⋊D13D311yescharacteristic, complemented
22C2×D52—31no—
23C2×C4×D13—31no—
24C13×C22⋊C4—31no—
25#6103—31no—
26#6101—31no—
27C22×C3×C13—21no—
28C22×C3×C13—21no—
29C22×C3×C13—21no—
30C22×C3×C13C2311yescharacteristic
31C2×D39—21no—
32C2×D39—21no—
33C2×D39—21no—
34C2×C3×D13—21no—
35C2×C3×D13—21no—
36C2×C3×D13D412yescomplemented
37Dic39D412yescomplemented
38C3×Dic13—21no—
39Dic3×C13—21no—
40Dic3×C13—21no—
41C23×C13C2×D311yescharacteristic
42C22×D13—31no—
43C22×D13C2×D311yescharacteristic
44C2×C4×C13—31no—
45C2×C4×C13—31no—
46C22⋊D13—22no—
47C22⋊D13—62no—
48C2×Dic13—31no—
49C2×Dic13C2×D311yescharacteristic
50D52—62no—
51C4×D13—62no—
52#939—131nomaximal, Hall
53C2×C3×C13—41no—
54C2×C3×C13C2×D411yescharacteristic
55C2×C3×C13C2×D411yescharacteristic
56C2×C3×C13#4111yescharacteristic
57D39—41no—
58C3×D13—22no—
59C22×C13—21no—
60C22×C13—21no—
61C22×C13—21no—
62C22×C13C22×D311yescharacteristic
63C2×D13—21no—
64C2×D13—21no—
65C2×D13—61no—
66C2×D13—61no—
67C2×D13—61no—
68C2×D13#6712yescomplemented
69C4×C13—61no—
70C4×C13—61no—
71Dic13—21no—
72Dic13—32no—
73C2×C3×D4—131no—
74C2×#67—131no—
75C2×#67—131no—
76C22×Dic3—131no—
77#217D1311yescharacteristic, complemented
78(C2×D3)⋊C4—131no—
79Dic3⋊C4—131no—
80C3×C13#12111yescharacteristic, complemented, Hall
81#121—391noSylow
82C2×C13—41no—
83C2×C13D3×D411yescharacteristic
84C2×C13#23711yescharacteristic
85C2×C13C2×#6711yescharacteristic
86D13—22no—
87D13—121no—
88C23×C3—131no—
89C23×C3C2×D1311yescharacteristic
90C22×D3—131no—
91C3×D4—262no—
92C2×C3×C4—131no—
93#67—262no—
94#67—262no—
95C2×Dic3—131no—
96C2×Dic3—262no—
97C2×Dic3C2×D1311yescharacteristic
98C2×Dic3C2×D1311yescharacteristic
99C2×D4—131no—
100C2×D4—391no—
101C2×D4—391no—
102C22×C4—391no—
103C4⋊C4—391no—
104C22⋊C4—31no—
105C22⋊C4—391no—
106C13#93911yescharacteristic, complemented, Sylow
107C22×C3—21no—
108C22×C3—21no—
109C22×C3—21no—
110C22×C3—132no—
111C22×C3—261no—
112C22×C3—261no—
113C22×C3C22×D1311yescharacteristic
114C2×D3—261no—
115C2×D3—261no—
116C2×D3—261no—
117C3×C4—261no—
118Dic3—21no—
119Dic3—21no—
120Dic3—132no—
121C23—131no—
122C23—391no—
123C23D3×D1311yescharacteristic
124D4—262no—
125D4—782no—
126D4—782no—
127C2×C4—31no—
128C2×C4—31no—
129C2×C4—131no—
130C2×C4—391no—
131C2×C4—782no—
132C2×C3—41no—
133C2×C3—262no—
134C2×C3#612711yescharacteristic
135C2×C3D4×D1311yescharacteristic
136C2×C3D4×D1311yescharacteristic
137D3—521no—
138C22—21no—
139C22—21no—
140C22—21no—
141C22—132no—
142C22—261no—
143C22—261no—
144C22—781no—
145C22—781no—
146C22—781no—
147C22C2×D3×D1311yescharacteristic
148C4—61no—
149C4—61no—
150C4—261no—
151C4—392no—
152C3#8813811yescharacteristic, complemented, Sylow
153C2—41no—
154C2—262no—
155C2—1561no—
156C2#1059774511yescharacteristic
157C2#67×D1311yescharacteristic
158C2#1059775611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D13
commutator, socle, cosocleC22×C3×C13C23
FittingC23×C3×C13C22
hypercenterC23D3×D13
hypocenterC3×C13#121
LCSG ▷ C22×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#64625C2semidirect
2. C2×C3×C22⋊D13C2semidirect
3. C2×#64603C2semidirect
4. C2×Dic3×D13C2semidirect
5. C13×#217C2semidirect
6. #10597612C2semidirect
7. #10597610C2semidirect
21. C2×C22⋊D13D3semidirect
36. C2×C3×D13D4semidirect
37. Dic39D4semidirect
68. C2×D13#67semidirect
77. #217D13semidirect
80. C3×C13#121semidirect
106. C13#939semidirect
152. C3#88138semidirect

Maximal subgroups

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

subgroupindex
C2×#646252
C2×C3×C22⋊D132
C2×#646032
C2×Dic3×D132
C13×#2172
#105976122
#105976102
#881383
#93913