Finite Group Databasebeta

← #11921000

Subgroups — #11921000

Order 1152.

426 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C3×C42×A4C211yesmaximal, characteristic
2C2×C3⋊(A4⋊C8)C212yesmaximal
3#73044—33nomaximal
4#71529—31nomaximal
5C2×C3×C4×A4C412yes—
6C2×C3×C4×A4C2211yescharacteristic
7C3⋊(A4⋊C8)C414yescomplemented
8#63630—41nomaximal
9C22×C3×C42D311yescharacteristic
10C42×A4D313yes—
11C2×A4⋊C8—36no—
12C2×#830—32no—
13C2×#803—31no—
14C2×#803—31no—
15#4524—32no—
16C22×C3×A4C2×C411yescharacteristic
17C3×C4×A4—22no—
18C3×C4×A4C2×C412yes—
19C32×C42—41no—
20C2×C3⋊(C3⋊C8)—42no—
21#1749—91noSylow
22C23×C3×C4Dic312yes—
23C23×C3×C4C2×D311yescharacteristic
24C2×C4×A4Dic316yes—
25C2×C4×A4C2×D313yes—
26C2×C3×C42—31no—
27C2×C3×C42—31no—
28C2×C3×C42—32no—
29C22×C3⋊C8—32no—
30C22×C3⋊C8—32no—
31A4⋊C8—312no—
32#830—34no—
33#830—34no—
34#803—62no—
35#803—61no—
36#803—61no—
37#803—123no—
38C2×C3×A4C4211yescharacteristic
39C2×C3×A4M1612yes—
40C2×C32×C4—42no—
41C2×C32×C4—41no—
42C3⋊(C3⋊C8)—44no—
43C22×C42C3⋊D311yescharacteristic
44C2×C22⋊C8—92no—
45C2×#97—91no—
46C2×#97—91no—
47#336—92no—
48C24×C3C2×Dic311yescharacteristic
49C22×A4C2×Dic313yes—
50C22×C3×C4—22no—
51C22×C3×C4—31no—
52C22×C3×C4—32no—
53C22×C3×C4—32no—
54C22×C3×C4—31no—
55C22×C3×C4—32no—
56C22×C3×C4—62no—
57C22×C3×C4C4×D312yes—
58C4×A4—26no—
59C4×A4C4×D316yes—
60C3×C42—32no—
61C3×C42—31no—
62C3×C42—43no—
63C3×C42—61no—
64C3×C42S411yescharacteristic
65C2×C3⋊C8—34no—
66C2×C3⋊C8—34no—
67C2×C3⋊C8—62no—
68C2×C3⋊C8—62no—
69C2×C3⋊C8—62no—
70C2×C3⋊C8—62no—
71C2×C3⋊C8—126no—
72C22×C32—41no—
73C3×A4#9711yescharacteristic, complemented
74C32×C4—42no—
75C32×C4—82no—
76C23×C4C3⋊Dic312yes—
77C23×C4C2×C3⋊D311yescharacteristic
78C22×C8—92no—
79C22×C8—92no—
80C2×C42—31no—
81C2×C42—31no—
82C2×C42—32no—
83C22⋊C8—94no—
84C22⋊C8—94no—
85#97—181no—
86#97—182no—
87#97—181no—
88C23×C3—31no—
89C23×C3—31no—
90C23×C3—32no—
91C23×C3#20812yes—
92C23×C3C4×Dic311yescharacteristic
93C2×A4#20816yes—
94C2×A4C4×Dic313yes—
95C2×C3×C4—31no—
96C2×C3×C4—32no—
97C2×C3×C4—32no—
98C2×C3×C4—32no—
99C2×C3×C4—34no—
100C2×C3×C4—32no—
101C2×C3×C4—43no—
102C2×C3×C4—46no—
103C2×C3×C4—62no—
104C2×C3×C4—62no—
105C2×C3×C4—61no—
106C2×C3×C4—62no—
107C2×C3×C4SL(2,ℤ/4)12yes—
108C2×C3×C4C2×S411yescharacteristic
109C3⋊C8—64no—
110C3⋊C8—64no—
111C3⋊C8—1212no—
112C2×C32—42no—
113C2×C32—41no—
114C24C2×C3⋊Dic311yescharacteristic
115C22×C4—22no—
116C22×C4—31no—
117C22×C4—32no—
118C22×C4—32no—
119C22×C4—31no—
120C22×C4—32no—
121C22×C4—62no—
122C22×C4C4×C3⋊D312yes—
123C2×C8—94no—
124C2×C8—94no—
125C2×C8—182no—
126C2×C8—182no—
127C2×C8—182no—
128C2×C8—182no—
129C42—31no—
130C42—32no—
131C42—61no—
132C42C3⋊S411yescharacteristic
133C22×C3—32no—
134C22×C3—31no—
135C22×C3—32no—
136C22×C3—32no—
137C22×C3—31no—
138C22×C3—31no—
139C22×C3—43no—
140C22×C3—61no—
141C22×C3#80311yescharacteristic, complemented
142C22×C3C2×SL(2,ℤ/4)11yescharacteristic
143A4#80313yescomplemented
144C3×C4—22no—
145C3×C4—32no—
146C3×C4—46no—
147C3×C4—62no—
148C3×C4—86no—
149C3×C4C4×S412yes—
150C32—41noSylow
151C23—31no—
152C23—31no—
153C23—32no—
154C23#374812yes—
155C23C4×C3⋊Dic311yescharacteristic
156C2×C4—31no—
157C2×C4—32no—
158C2×C4—32no—
159C2×C4—32no—
160C2×C4—34no—
161C2×C4—32no—
162C2×C4—62no—
163C2×C4—62no—
164C2×C4—61no—
165C2×C4—62no—
166C2×C4C3⋊SL(2,ℤ/4)12yes—
167C2×C4C2×C3⋊S411yescharacteristic
168C8—184no—
169C8—184no—
170C2×C3—31no—
171C2×C3—32no—
172C2×C3—31no—
173C2×C3—46no—
174C2×C3—43no—
175C2×C3#540912yes—
176C2×C3C4×SL(2,ℤ/4)11yescharacteristic
177C22—32no—
178C22—31no—
179C22—32no—
180C22—32no—
181C22—31no—
182C22—31no—
183C22—61no—
184C22#6363011yescharacteristic, complemented
185C22C2×C3⋊SL(2,ℤ/4)11yescharacteristic
186C4—22no—
187C4—32no—
188C4—62no—
189C4C4×C3⋊S412yes—
190C3—43no—
191C3#7304411yescharacteristic, complemented
192C2—31no—
193C2—32no—
194C2—31no—
195C2#1059364312yes—
196C2C4×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×C3⋊S4
commutatorC2×C3×A4C42
FittingC22×C3×C42D3
socleC24×C3C2×Dic3
prime radicalC22×C3×A4C2×C4
cosocleC2×C3×C4×A4C22
hypercenterC42C3⋊S4
hypocenterC3×A4#97
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
7. C3⋊(A4⋊C8)C4semidirect
73. C3×A4#97semidirect
141. C22×C3#803semidirect
143. A4#803semidirect
184. C22#63630semidirect
191. C3#73044semidirect

Maximal subgroups

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

subgroupindex
C3×C42×A42
C2×C3⋊(A4⋊C8)2
#730443
#715293
#636304