Finite Group Databasebeta

← #11920590

Subgroups — #11920590

Order 1152.

226 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 31 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
1A4×Dic12C211yesmaximal, characteristic, complemented
2#10593636C211yesmaximal, characteristic
3C3×A4⋊C16C211yesmaximal, characteristic, complemented
4#73135—31nomaximal
5#69112—31nomaximal
6A4×Dic6—21no—
7C4⋊(C3⋊S4)—21no—
8C3×C8×A4C2211yescharacteristic
9#63549—41nomaximal
10C22×Dic12D311yescharacteristic, complemented
11A4×Q16—31no—
12#5402—31no—
13#5402—61no—
14#5115—31no—
15C2×#800—31no—
16C2×#800—31no—
17A4⋊C16D311yescharacteristic, complemented
18C3×C22⋊C16—31no—
19#4503—31no—
20#4503—31no—
21C2×C3⋊S4—41no—
22C3×C4×A4D411yescharacteristic
23Dic3×A4—41no—
24#3745—41no—
25C3×Dic12—41no—
26C3×C3⋊C16—41no—
27#2185—91noSylow
28C22×Dic6—21no—
29Q8×A4—61no—
30C4⋊S4—62no—
31C4⋊S4—61no—
32C22×C3×C8C2×D311yescharacteristic
33#930—61no—
34C2×Dic12—31no—
35C2×Dic12—31no—
36C2×Dic12—61no—
37C2×D24—31no—
38C8×A4—21no—
39C8×A4C2×D311yescharacteristic
40C2×C3×C16—31no—
41C2×C3×C16—31no—
42#828—121no—
43#821—61no—
44#818—31no—
45#800—62no—
46#800—61no—
47#800—61no—
48C2×C3×A4D811yescharacteristic
49C3⋊S4—81no—
50C4⋊(C3⋊D3)—81no—
51C3×Dic6—81no—
52C32×C8—41no—
53C22×Q16—31no—
54C2×SD32—91no—
55C2×SD32—91no—
56#466—91no—
57#358—91no—
58#358—91no—
59C22⋊C16—31no—
60C2×S4—122no—
61C2×S4—121no—
62C22×C3×C4#6711yescharacteristic
63C2×#67—121no—
64C22×Dic3—41no—
65C2×D12—61no—
66C2×Dic6—61no—
67C2×Dic6—61no—
68C2×Dic6—121no—
69C4×A4—21no—
70C4×A4—121no—
71C4×A4D1211yescharacteristic
72C3×Q16—121no—
73C2×C3×C8—31no—
74C2×C3×C8—31no—
75(C2×D3)⋊C4—121no—
76C4⋊Dic3—61no—
77Dic12—32no—
78Dic12—31no—
79Dic12—61no—
80Dic12S411yescharacteristic, complemented
81D24—61no—
82D24—61no—
83D24—121no—
84D24—241no—
85C3×C16—61no—
86C3×C16—61no—
87C3⋊C16—41no—
88C2×C3⋊D3—161no—
89C3×A4SD3211yescharacteristic, complemented
90C32×C4—41no—
91C3×Dic3—161no—
92C22×Q8—61no—
93C2×Q16—91no—
94C2×Q16—91no—
95C2×Q16—181no—
96C2×D8—91no—
97C22×C8D3211yescharacteristic
98#121—181no—
99SD32—181no—
100SD32—182no—
101SD32—181no—
102C2×C16—31no—
103C2×C16—31no—
104#107—91no—
105#102—181no—
106C23×C3#21311yescharacteristic
107C22×D3—121no—
108C2×A4—21no—
109C2×A4D2411yescharacteristic
110S4—242no—
111S4—241no—
112C3×Q8—241no—
113C2×C3×C4—31no—
114C2×C3×C4—31no—
115#67—241no—
116#67—241no—
117C2×Dic3—121no—
118C2×Dic3—121no—
119C2×Dic3—121no—
120D12—121no—
121D12—121no—
122D12—241no—
123D12—242no—
124Dic6—21no—
125Dic6—61no—
126Dic6—121no—
127Dic6—121no—
128C3×C8—31no—
129C3×C8—41no—
130C3×C8—81no—
131C3×C8C2×S411yescharacteristic
132C2×C32—41no—
133C3⋊D3—321no—
134C2×Q8—181no—
135C2×Q8—181no—
136C2×Q8—361no—
137C2×D4—181no—
138C2×D4—361no—
139C22×C4—121no—
140C22×C4#62611yescharacteristic
141Q16—31no—
142Q16—92no—
143Q16—91no—
144Q16—181no—
145D8—181no—
146D8—181no—
147C2×C8—31no—
148C2×C8—31no—
149C4⋊C4—181no—
150C22⋊C4—361no—
151C16—61no—
152C16—61no—
153C22×C3—31no—
154C22×C3—31no—
155C22×C3#82811yescharacteristic, complemented
156C2×D3—241no—
157C2×D3—241no—
158C2×D3—241no—
159C2×D3—481no—
160C2×D3—482no—
161A4—21no—
162A4#80011yescharacteristic, complemented
163C3×C4—31no—
164C3×C4—41no—
165C3×C4—81no—
166C3×C4—481no—
167C3×C4GL(2,ℤ/4)11yescharacteristic
168Dic3—41no—
169Dic3—121no—
170Dic3—241no—
171C32—41noSylow
172C23—361no—
173C23#371411yescharacteristic
174Q8—61no—
175Q8—181no—
176Q8—361no—
177Q8—361no—
178D4—361no—
179D4—361no—
180D4—721no—
181D4—721no—
182C2×C4—31no—
183C2×C4—31no—
184C2×C4—361no—
185C2×C4—361no—
186C2×C4—361no—
187C8—31no—
188C8D3×S411yescharacteristic
189C2×C3—31no—
190C2×C3—31no—
191C2×C3—41no—
192C2×C3—81no—
193C2×C3#541511yescharacteristic
194D3—481no—
195D3—961no—
196D3—962no—
197C22—31no—
198C22—31no—
199C22—721no—
200C22—721no—
201C22—721no—
202C22#6354911yescharacteristic, complemented
203C4—31no—
204C4—121no—
205C4—361no—
206C4—721no—
207C4#6421011yescharacteristic
208C3—41no—
209C3—81no—
210C3#7313511yescharacteristic, complemented
211C2—31no—
212C2—31no—
213C2—1441no—
214C2#1059318411yescharacteristic
subgroupG/H
centerC2#10593184
commutator, cosocleC3×C8×A4C22
Frattini, hypercenterC8D3×S4
FittingC22×C3×C8C2×D3
socleC23×C3#213
prime radical#10593636C2
hypocenterC3×A4SD32
LCSG ▷ C3×C8×A4 ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
1. A4×Dic12C2semidirect
3. C3×A4⋊C16C2semidirect
10. C22×Dic12D3semidirect
17. A4⋊C16D3semidirect
80. Dic12S4semidirect
89. C3×A4SD32semidirect
155. C22×C3#828semidirect
162. A4#800semidirect
202. C22#63549semidirect
210. C3#73135semidirect

Maximal subgroups

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

subgroupindex
A4×Dic122
#105936362
C3×A4⋊C162
#731353
#691123
#635494