Finite Group Databasebeta

← C3×#88193 #11928822

Subgroups — C3×#88193 #11928822

Order 1248.

188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 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×D4×C13C211yesmaximal, characteristic, complemented
2C2×C3×C22⋊D13C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊D13C211yesmaximal, characteristic, complemented
4C22×C3×Dic13C211yesmaximal, characteristic, complemented
5C3×C22⋊Dic13C211yesmaximal, characteristic, complemented
6C3×#6103C211yesmaximal, characteristic, complemented
7C3×#6101C211yesmaximal, characteristic, complemented
8#88193C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×C13C2211yescharacteristic
10C23×C3×C13C2211yescharacteristic
11C22×C3×D13C2211yescharacteristic
12C3×D4×C13—22no—
13C2×C3×C4×C13C2211yescharacteristic
14C3×C22⋊D13—22no—
15C3×C22⋊D13—22no—
16C2×C3×Dic13—22no—
17C2×C3×Dic13C2211yescharacteristic
18C2×C3×Dic13C2211yescharacteristic
19C2×C3×Dic13C2211yescharacteristic
20C2×D4×C13C2×C311yescharacteristic, complemented
21C2×C22⋊D13C2×C311yescharacteristic, complemented
22C2×C22⋊D13C2×C311yescharacteristic, complemented
23C22×Dic13C2×C311yescharacteristic, complemented
24C22⋊Dic13C2×C311yescharacteristic, complemented
25#6103C2×C311yescharacteristic, complemented
26#6101C2×C311yescharacteristic, complemented
27C22×C3×C13—21no—
28C22×C3×C13—21no—
29C22×C3×C13—21no—
30C22×C3×C13—21no—
31C22×C3×C13—21no—
32C22×C3×C13D412yescomplemented
33C22×C3×C13C2311yescharacteristic
34C2×C3×D13—21no—
35C2×C3×D13—21no—
36C2×C3×D13—21no—
37C3×C4×C13—21no—
38C3×Dic13—21no—
39C3×Dic13—21no—
40C3×Dic13D412yescomplemented
41C23×C13C22×C311yescharacteristic
42C23×C13C22×C311yescharacteristic
43C22×D13C22×C311yescharacteristic
44D4×C13—22no—
45C2×C4×C13C22×C311yescharacteristic
46C22⋊D13—22no—
47C22⋊D13—22no—
48C2×Dic13—22no—
49C2×Dic13C22×C311yescharacteristic
50C2×Dic13C22×C311yescharacteristic
51C2×Dic13C22×C311yescharacteristic
52C3×#121—131nomaximal, Hall
53C2×C3×C13—22no—
54C2×C3×C13—41no—
55C2×C3×C13C2×D411yescharacteristic
56C2×C3×C13C2×D411yescharacteristic
57C2×C3×C13#4111yescharacteristic
58C3×D13—41no—
59C22×C13—21no—
60C22×C13—21no—
61C22×C13—21no—
62C22×C13—21no—
63C22×C13—21no—
64C22×C13C3×D412yescomplemented
65C22×C13C23×C311yescharacteristic
66C2×D13—21no—
67C2×D13—21no—
68C2×D13—21no—
69C4×C13—21no—
70Dic13—21no—
71Dic13—21no—
72Dic13C3×D412yescomplemented
73C2×C3×D4—131no—
74C2×C3×D4—131no—
75C2×C3×D4D1311yescharacteristic, complemented
76C22×C3×C4—131no—
77C3×C4⋊C4—131no—
78C3×C22⋊C4—131no—
79C3×C22⋊C4—131no—
80C3×C13#12111yescharacteristic, complemented, Hall
81#121—131noSylow
82C2×C13—22no—
83C2×C13—41no—
84C2×C13C2×C3×D411yescharacteristic
85C2×C13C2×C3×D411yescharacteristic
86C2×C13C3×#4111yescharacteristic
87D13—41no—
88C23×C3—131no—
89C23×C3C2×D1311yescharacteristic
90C23×C3C2×D1311yescharacteristic
91C3×D4—22no—
92C3×D4—262no—
93C3×D4—262no—
94C2×C3×C4—131no—
95C2×C3×C4—131no—
96C2×C3×C4—131no—
97C2×C3×C4—262no—
98C2×C3×C4C2×D1311yescharacteristic
99C2×D4—131no—
100C2×D4—131no—
101C2×D4C3×D1311yescharacteristic, complemented
102C22×C4—131no—
103C4⋊C4—131no—
104C22⋊C4—131no—
105C22⋊C4—131no—
106C13C3×#12111yescharacteristic, complemented, Sylow
107C22×C3—21no—
108C22×C3—21no—
109C22×C3—21no—
110C22×C3—21no—
111C22×C3—21no—
112C22×C3—261no—
113C22×C3—261no—
114C22×C3—261no—
115C22×C3C22⋊D1312yescomplemented
116C22×C3C22×D1311yescharacteristic
117C3×C4—21no—
118C3×C4—132no—
119C3×C4—261no—
120C3×C4—261no—
121C23—131no—
122C23C2×C3×D1311yescharacteristic
123C23C2×C3×D1311yescharacteristic
124D4—22no—
125D4—262no—
126D4—262no—
127C2×C4—131no—
128C2×C4—131no—
129C2×C4—131no—
130C2×C4—262no—
131C2×C4C2×C3×D1311yescharacteristic
132C2×C3—22no—
133C2×C3—41no—
134C2×C3—521no—
135C2×C3D4×D1311yescharacteristic
136C2×C3#612911yescharacteristic
137C2×C3C2×C22⋊D1311yescharacteristic
138C22—21no—
139C22—21no—
140C22—21no—
141C22—21no—
142C22—21no—
143C22—261no—
144C22—261no—
145C22—261no—
146C22C3×C22⋊D1312yescomplemented
147C22C22×C3×D1311yescharacteristic
148C4—21no—
149C4—132no—
150C4—261no—
151C4—261no—
152C3#8819311yescharacteristic, direct product factor, Sylow
153C2—22no—
154C2—41no—
155C2—521no—
156C2C3×D4×D1311yescharacteristic
157C2C3×#612911yescharacteristic
158C2C2×C3×C22⋊D1311yescharacteristic
subgroupG/H
centerC22×C3C22×D13
commutator, cosocleC22×C13C23×C3
FrattiniC22C22×C3×D13
FittingC2×C3×D4×C13C2
socleC22×C3×C13C23
hypercenterC2×C3×D4D13
hypocenterC13C3×#121
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C13C2semidirect
2. C2×C3×C22⋊D13C2semidirect
3. C2×C3×C22⋊D13C2semidirect
4. C22×C3×Dic13C2semidirect
5. C3×C22⋊Dic13C2semidirect
6. C3×#6103C2semidirect
7. C3×#6101C2semidirect
8. #88193C3direct (N × H)
20. C2×D4×C13C2×C3semidirect
21. C2×C22⋊D13C2×C3semidirect
22. C2×C22⋊D13C2×C3semidirect
23. C22×Dic13C2×C3semidirect
24. C22⋊Dic13C2×C3semidirect
25. #6103C2×C3semidirect
26. #6101C2×C3semidirect
32. C22×C3×C13D4semidirect
40. C3×Dic13D4semidirect
64. C22×C13C3×D4semidirect
72. Dic13C3×D4semidirect
75. C2×C3×D4D13semidirect
80. C3×C13#121semidirect
101. C2×D4C3×D13semidirect
106. C13C3×#121semidirect
115. C22×C3C22⋊D13semidirect
146. C22C3×C22⋊D13semidirect
152. C3#88193direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×C132
C2×C3×C22⋊D132
C22×C3×Dic132
C3×C22⋊Dic132
C3×#61032
C3×#61012
#881933
C3×#12113