Finite Group Databasebeta

← #72241981

Subgroups — #72241981

Order 2808.

188 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 38 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⋊(C3⋊(D13⋊C3))C211yesmaximal, characteristic, complemented
2C2×C3×C3⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C3×Dic3×C13⋊C3C211yesmaximal, characteristic, complemented
4#11745533C311yesmaximal, characteristic, complemented
5C4⋊(C3⋊(D13⋊C3))—31nomaximal
6#64603⋊C3—31nomaximal
7C2×C32×C13⋊C3C2211yescharacteristic
8C3⋊(C3⋊(D13⋊C3))—21no—
9C3×C3⋊(D13⋊C3)—21no—
10C2×C3⋊D39C2×C311yescharacteristic, complemented
11C2×C3×D39C2×C311yescharacteristic, complemented
12C2×C3⋊(D13⋊C3)—21no—
13C2×C3⋊(D13⋊C3)—31no—
14C2×C3⋊(D13⋊C3)—31no—
15C2×C3⋊(D13⋊C3)—61no—
16C2×C3⋊(D13⋊C3)D311yescharacteristic, complemented
17C2×C3×D13⋊C3—31no—
18C3×Dic3×C13C2×C311yescharacteristic, complemented
19C3×C4×C13⋊C3—31no—
20Dic3×C13⋊C3—21no—
21Dic3×C13⋊C3D311yescharacteristic, complemented
22C32×C13⋊C3D411yescharacteristic, complemented, Hall
23D156—31no—
24#64603—31no—
25C4⋊(D13⋊C3)—91no—
26C2×C32×C13C22×C311yescharacteristic
27C3⋊D39—21no—
28C3×D39—21no—
29C2×C3×C13⋊C3—21no—
30C2×C3×C13⋊C3—21no—
31C2×C3×C13⋊C3—21no—
32C2×C3×C13⋊C3—41no—
33C2×C3×C13⋊C3C2×D311yescharacteristic
34C2×C3×C13⋊C3C2×D311yescharacteristic
35C3⋊(D13⋊C3)—21no—
36C3⋊(D13⋊C3)—21no—
37C3⋊(D13⋊C3)—21no—
38C3⋊(D13⋊C3)—61no—
39C3⋊(D13⋊C3)—61no—
40C3⋊(D13⋊C3)—61no—
41C3⋊(D13⋊C3)—61no—
42C3×D13⋊C3—61no—
43C3×#626—131nomaximal, Hall
44C2×D39—31no—
45C2×D39—31no—
46C2×D39—61no—
47C2×D39C3×D311yescharacteristic, complemented
48C2×C3×D13—31no—
49C2×D13⋊C3—31no—
50C2×D13⋊C3—61no—
51C2×D13⋊C3—91no—
52C3×C4×C13—31no—
53Dic3×C13C3×D311yescharacteristic, complemented
54C4×C13⋊C3—31no—
55C4×C13⋊C3—61no—
56C32×C13C3×D411yescharacteristic, complemented
57C3×C13⋊C3—21no—
58C3×C13⋊C3—21no—
59C3×C13⋊C3—21no—
60C3×C13⋊C3—41no—
61C3×C13⋊C3D1211yescharacteristic, complemented
62C3×C13⋊C3#6711yescharacteristic, complemented
63C2×C3×C3⋊D3—131no—
64C2×C32×D3—131no—
65C32×Dic3—261no—
66D52—91noHall
67C2×C3×C13—21no—
68C2×C3×C13C2×C3×D311yescharacteristic
69C2×C3×C13C2×C3×D311yescharacteristic
70D39—21no—
71D39—61no—
72D39—61no—
73D39—61no—
74D39—61no—
75C3×D13—61no—
76C2×C13⋊C3—21no—
77C2×C13⋊C3—21no—
78C2×C13⋊C3—41no—
79C2×C13⋊C3D3211yescharacteristic
80D13⋊C3—61no—
81D13⋊C3—61no—
82D13⋊C3—61no—
83D13⋊C3—181no—
84C3×#67—391no—
85C3×D12—391no—
86#626—131no—
87C2×C33—261no—
88C3×C3⋊D3—261no—
89C32×D3—261no—
90C2×D13—31no—
91C2×D13—91no—
92C4×C13—31no—
93C3×C13—21no—
94C3×C13C3×D1211yescharacteristic, complemented
95C3×C13C3×#6711yescharacteristic, complemented
96C13⋊C3—21no—
97C13⋊C3—21no—
98C13⋊C3—41no—
99C13⋊C3#62611yescharacteristic, complemented
100C22×C32—391no—
101C2×C3⋊D3—131no—
102C2×C3×D3—131no—
103C2×C3×D3—131no—
104C2×C3×D3—261no—
105C2×C3×D3—391no—
106C2×C3×D3—391no—
107C2×C3×D3—781no—
108C32×C4—781no—
109C3×Dic3—261no—
110C3×Dic3—261no—
111C3×Dic3D13⋊C311yescharacteristic, complemented
112C33—261noSylow
113C2×C13C3×D3211yescharacteristic
114D13—61no—
115D13—181no—
116C3×D4—1171no—
117#67—391no—
118D12—391no—
119C2×C32—261no—
120C2×C32—261no—
121C2×C32—261no—
122C2×C32—261no—
123C2×C32—521no—
124C2×C32—521no—
125C2×C32—781no—
126C2×C32C2×D13⋊C311yescharacteristic
127C3⋊D3—261no—
128C3×D3—261no—
129C3×D3—261no—
130C3×D3—261no—
131C3×D3—261no—
132C3×D3—781no—
133C3×D3—781no—
134C3×D3—781no—
135C3×D3—781no—
136C13C3×#62611yescharacteristic, complemented, Sylow
137C22×C3—391no—
138C22×C3—391no—
139C22×C3—781no—
140C22×C3—1171no—
141C2×D3—131no—
142C2×D3—391no—
143C2×D3—391no—
144C2×D3—781no—
145C3×C4—31no—
146C3×C4—781no—
147C3×C4—781no—
148Dic3C3⋊(D13⋊C3)11yescharacteristic, complemented
149C32—261no—
150C32—261no—
151C32—261no—
152C32—261no—
153C32—521no—
154C32—521no—
155C32C4⋊(D13⋊C3)11yescharacteristic, complemented
156D4—1171noSylow
157C2×C3—21no—
158C2×C3—261no—
159C2×C3—261no—
160C2×C3—521no—
161C2×C3—521no—
162C2×C3—781no—
163C2×C3—781no—
164C2×C3—781no—
165C2×C3—781no—
166C2×C3—2341no—
167C2×C3D3×D13⋊C311yescharacteristic
168C2×C3C2×C3⋊(D13⋊C3)11yescharacteristic
169D3—261no—
170D3—781no—
171D3—781no—
172D3—781no—
173D3—781no—
174C22—391no—
175C22—1171no—
176C4—31no—
177C3—21no—
178C3—261no—
179C3—261no—
180C3—521no—
181C3—521no—
182C3#64603⋊C311yescharacteristic, complemented
183C3C4⋊(C3⋊(D13⋊C3))11yescharacteristic, complemented
184C2—781no—
185C2—2341no—
186C2D3×C3⋊(D13⋊C3)11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×C3⋊(D13⋊C3)
commutator, Fitting, socle, cosocleC2×C32×C13C22×C3
hypocenterC32×C13C3×D4
LCSG ▷ C2×C32×C13 ▷ C32×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊(C3⋊(D13⋊C3))C2semidirect
2. C2×C3×C3⋊(D13⋊C3)C2semidirect
3. C3×Dic3×C13⋊C3C2semidirect
4. #11745533C3semidirect
10. C2×C3⋊D39C2×C3semidirect
11. C2×C3×D39C2×C3semidirect
16. C2×C3⋊(D13⋊C3)D3semidirect
18. C3×Dic3×C13C2×C3semidirect
21. Dic3×C13⋊C3D3semidirect
22. C32×C13⋊C3D4semidirect
47. C2×D39C3×D3semidirect
53. Dic3×C13C3×D3semidirect
56. C32×C13C3×D4semidirect
61. C3×C13⋊C3D12semidirect
62. C3×C13⋊C3#67semidirect
94. C3×C13C3×D12semidirect
95. C3×C13C3×#67semidirect
99. C13⋊C3#626semidirect
111. C3×Dic3D13⋊C3semidirect
136. C13C3×#626semidirect
148. Dic3C3⋊(D13⋊C3)semidirect
155. C32C4⋊(D13⋊C3)semidirect
182. C3#64603⋊C3semidirect
183. C3C4⋊(C3⋊(D13⋊C3))semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(C3⋊(D13⋊C3))2
C2×C3×C3⋊(D13⋊C3)2
C3×Dic3×C13⋊C32
#117455333
C4⋊(C3⋊(D13⋊C3))3
#64603⋊C33
C3×#62613