Finite Group Databasebeta

← C3×#88138 #11928775

Subgroups — C3×#88138 #11928775

Order 1248.

188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 66 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×C3×C22⋊D13C211yesmaximal, characteristic, complemented
2C2×C3×C22⋊D13C211yesmaximal, characteristic, complemented
3C2×C3×D52C211yesmaximal, characteristic, complemented
4C2×C3×C4×D13C211yesmaximal, characteristic, complemented
5C3×C13×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#6103C211yesmaximal, characteristic, complemented
7C3×#6101C211yesmaximal, characteristic, complemented
8#88138C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×C13C2211yescharacteristic
10C22×C3×D13C2211yescharacteristic
11C22×C3×D13C2211yescharacteristic
12C2×C3×C4×C13C2211yescharacteristic
13C2×C3×C4×C13C2211yescharacteristic
14C3×C22⋊D13—22no—
15C3×C22⋊D13—22no—
16C2×C3×Dic13C2211yescharacteristic
17C2×C3×Dic13C2211yescharacteristic
18C3×D52—22no—
19C3×C4×D13—22no—
20C2×C22⋊D13C2×C311yescharacteristic, complemented
21C2×C22⋊D13C2×C311yescharacteristic, complemented
22C2×D52C2×C311yescharacteristic, complemented
23C2×C4×D13C2×C311yescharacteristic, complemented
24C13×C22⋊C4C2×C311yescharacteristic, complemented
25#6103C2×C311yescharacteristic, complemented
26#6101C2×C311yescharacteristic, complemented
27C22×C3×C13—21no—
28C22×C3×C13—21no—
29C22×C3×C13—21no—
30C22×C3×C13C2311yescharacteristic
31C2×C3×D13—21no—
32C2×C3×D13—21no—
33C2×C3×D13—21no—
34C2×C3×D13—21no—
35C2×C3×D13—21no—
36C2×C3×D13D412yescomplemented
37C3×C4×C13—21no—
38C3×C4×C13—21no—
39C3×Dic13—21no—
40C3×Dic13D412yescomplemented
41C23×C13C22×C311yescharacteristic
42C22×D13C22×C311yescharacteristic
43C22×D13C22×C311yescharacteristic
44C2×C4×C13C22×C311yescharacteristic
45C2×C4×C13C22×C311yescharacteristic
46C22⋊D13—22no—
47C22⋊D13—22no—
48C2×Dic13C22×C311yescharacteristic
49C2×Dic13C22×C311yescharacteristic
50D52—22no—
51C4×D13—22no—
52C3×#121—131nomaximal, Hall
53C2×C3×C13—41no—
54C2×C3×C13C2×D411yescharacteristic
55C2×C3×C13C2×D411yescharacteristic
56C2×C3×C13#4111yescharacteristic
57C3×D13—22no—
58C3×D13—41no—
59C22×C13—21no—
60C22×C13—21no—
61C22×C13—21no—
62C22×C13C23×C311yescharacteristic
63C2×D13—21no—
64C2×D13—21no—
65C2×D13—21no—
66C2×D13—21no—
67C2×D13—21no—
68C2×D13C3×D412yescomplemented
69C4×C13—21no—
70C4×C13—21no—
71Dic13—21no—
72Dic13C3×D412yescomplemented
73C2×C3×D4—131no—
74C2×C3×D4—131no—
75C2×C3×D4—131no—
76C22×C3×C4—131no—
77C3×C4⋊C4—131no—
78C3×C22⋊C4—131no—
79C3×C22⋊C4D1311yescharacteristic, complemented
80C3×C13#12111yescharacteristic, complemented, Hall
81#121—131noSylow
82C2×C13—41no—
83C2×C13C2×C3×D411yescharacteristic
84C2×C13C2×C3×D411yescharacteristic
85C2×C13C3×#4111yescharacteristic
86D13—22no—
87D13—41no—
88C23×C3—131no—
89C23×C3—131no—
90C23×C3C2×D1311yescharacteristic
91C3×D4—262no—
92C3×D4—262no—
93C3×D4—262no—
94C2×C3×C4—131no—
95C2×C3×C4—131no—
96C2×C3×C4—262no—
97C2×C3×C4C2×D1311yescharacteristic
98C2×C3×C4C2×D1311yescharacteristic
99C2×D4—131no—
100C2×D4—131no—
101C2×D4—131no—
102C22×C4—131no—
103C4⋊C4—131no—
104C22⋊C4—131no—
105C22⋊C4C3×D1311yescharacteristic, complemented
106C13C3×#12111yescharacteristic, complemented, Sylow
107C22×C3—21no—
108C22×C3—21no—
109C22×C3—21no—
110C22×C3—132no—
111C22×C3—261no—
112C22×C3—261no—
113C22×C3—261no—
114C22×C3—261no—
115C22×C3—261no—
116C22×C3C22×D1311yescharacteristic
117C3×C4—21no—
118C3×C4—21no—
119C3×C4—132no—
120C3×C4—261no—
121C23—131no—
122C23—131no—
123C23C2×C3×D1311yescharacteristic
124D4—262no—
125D4—262no—
126D4—262no—
127C2×C4—131no—
128C2×C4—131no—
129C2×C4—262no—
130C2×C4C2×C3×D1311yescharacteristic
131C2×C4C2×C3×D1311yescharacteristic
132C2×C3—41no—
133C2×C3—262no—
134C2×C3—521no—
135C2×C3#612711yescharacteristic
136C2×C3D4×D1311yescharacteristic
137C2×C3D4×D1311yescharacteristic
138C22—21no—
139C22—21no—
140C22—21no—
141C22—132no—
142C22—261no—
143C22—261no—
144C22—261no—
145C22—261no—
146C22—261no—
147C22C22×C3×D1311yescharacteristic
148C4—21no—
149C4—21no—
150C4—132no—
151C4—261no—
152C3#8813811yescharacteristic, direct product factor, Sylow
153C2—41no—
154C2—262no—
155C2—521no—
156C2C3×#612711yescharacteristic
157C2C3×D4×D1311yescharacteristic
158C2C3×D4×D1311yescharacteristic
subgroupG/H
centerC22×C3C22×D13
commutator, cosocleC22×C13C23×C3
FrattiniC22C22×C3×D13
FittingC3×C13×C22⋊C4C2
socleC22×C3×C13C23
hypercenterC3×C22⋊C4D13
hypocenterC13C3×#121
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C22⋊D13C2semidirect
2. C2×C3×C22⋊D13C2semidirect
3. C2×C3×D52C2semidirect
4. C2×C3×C4×D13C2semidirect
5. C3×C13×C22⋊C4C2semidirect
6. C3×#6103C2semidirect
7. C3×#6101C2semidirect
8. #88138C3direct (N × H)
20. C2×C22⋊D13C2×C3semidirect
21. C2×C22⋊D13C2×C3semidirect
22. C2×D52C2×C3semidirect
23. C2×C4×D13C2×C3semidirect
24. C13×C22⋊C4C2×C3semidirect
25. #6103C2×C3semidirect
26. #6101C2×C3semidirect
36. C2×C3×D13D4semidirect
40. C3×Dic13D4semidirect
68. C2×D13C3×D4semidirect
72. Dic13C3×D4semidirect
79. C3×C22⋊C4D13semidirect
80. C3×C13#121semidirect
105. C22⋊C4C3×D13semidirect
106. C13C3×#121semidirect
152. C3#88138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C22⋊D132
C2×C3×D522
C2×C3×C4×D132
C3×C13×C22⋊C42
C3×#61032
C3×#61012
#881383
C3×#12113