Finite Group Databasebeta

← #11921061

Subgroups — #11921061

Order 1152.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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×C8×A4C211yesmaximal, characteristic
2#10593643C212yesmaximal
3#73105—33nomaximal
4#71977—31nomaximal
5C2×C3×C4×A4C2211yescharacteristic
6C3×C8×A4C412yes—
7C3⋊(A4⋊C8)—22no—
8#63646—41nomaximal
9C23×C3×C8D311yescharacteristic
10C2×C8×A4D313yes—
11#5409—36no—
12#5207—32no—
13C2×#819—31no—
14C2×#819—31no—
15#4552—32no—
16C22×C3×A4Q811yescharacteristic
17C3×C4×A4C2×C411yescharacteristic
18C3×C4×A4D411yescharacteristic
19C2×C32×C8—41no—
20#3748—42no—
21#1810—91noSylow
22C23×C3×C4C2×D311yescharacteristic
23C2×C4×A4C2×D313yes—
24C22×C3×C8—31no—
25C22×C3×C8—32no—
26C22×C3×C8—31no—
27C22×C3×C8Dic312yes—
28C2×#208—32no—
29C2×#208—32no—
30C8×A4Dic316yes—
31A4⋊C8—66no—
32#830—62no—
33#830—62no—
34#819—62no—
35#819—61no—
36#819—61no—
37#819—123no—
38C2×C3×A4—21no—
39C2×C3×A4C4⋊C411yescharacteristic
40C2×C32×C4—41no—
41C32×C8—42no—
42C3⋊(C3⋊C8)—82no—
43C23×C8C3⋊D311yescharacteristic
44C2×#108—91no—
45C2×#108—91no—
46#407—92no—
47#341—92no—
48C24×C3Dic611yescharacteristic
49C22×A4Dic613yes—
50C22×C3×C4—31no—
51C22×C3×C4—31no—
52C22×C3×C4—31no—
53C22×C3×C4—31no—
54C22×C3×C4D1211yescharacteristic
55C22×C3×C4C2×Dic311yescharacteristic
56C4×A4D1213yes—
57C4×A4C2×Dic313yes—
58C2×C3×C8—31no—
59C2×C3×C8—32no—
60C2×C3×C8—32no—
61C2×C3×C8—32no—
62C2×C3×C8—43no—
63C2×C3×C8—61no—
64C2×C3×C8S411yescharacteristic
65#208—62no—
66#208—62no—
67#208—62no—
68#208—62no—
69#208—126no—
70C2×C3⋊C8—62no—
71C2×C3⋊C8—62no—
72C22×C32—41no—
73C3×A4#10811yescharacteristic, complemented
74C32×C4—41no—
75C32×C4—41no—
76C23×C4C2×C3⋊D311yescharacteristic
77C2×M16—92no—
78C2×M16—92no—
79C22×C8—31no—
80C22×C8—31no—
81C22×C8—32no—
82C22×C8C3⋊Dic312yes—
83#108—181no—
84#108—182no—
85#108—181no—
86C22⋊C8—182no—
87C22⋊C8—182no—
88C23×C3—21no—
89C23×C3—31no—
90C23×C3—31no—
91C23×C3—61no—
92C23×C3C4⋊Dic311yescharacteristic
93C2×A4—23no—
94C2×A4C4⋊Dic313yes—
95C2×C3×C4—31no—
96C2×C3×C4—31no—
97C2×C3×C4—31no—
98C2×C3×C4—31no—
99C2×C3×C4—31no—
100C2×C3×C4—31no—
101C2×C3×C4—31no—
102C2×C3×C4—43no—
103C2×C3×C4—61no—
104C2×C3×C4C2×S411yescharacteristic
105C3×C8—32no—
106C3×C8—46no—
107C3×C8SL(2,ℤ/4)12yes—
108C3⋊C8—122no—
109C3⋊C8—122no—
110C3⋊C8—246no—
111C2×C32—41no—
112C2×C32—81no—
113C24#63411yescharacteristic
114C22×C4—31no—
115C22×C4—31no—
116C22×C4—31no—
117C22×C4—31no—
118C22×C4C4⋊(C3⋊D3)11yescharacteristic
119C22×C4C2×C3⋊Dic311yescharacteristic
120M16—182no—
121M16—182no—
122M16—182no—
123M16—182no—
124C2×C8—31no—
125C2×C8—32no—
126C2×C8—32no—
127C2×C8—32no—
128C2×C8—61no—
129C2×C8—182no—
130C2×C8—182no—
131C2×C8C3⋊S411yescharacteristic
132C22×C3—31no—
133C22×C3—31no—
134C22×C3—32no—
135C22×C3—31no—
136C22×C3—43no—
137C22×C3—61no—
138C22×C3—61no—
139C22×C3—61no—
140C22×C3#81911yescharacteristic, complemented
141C22×C3A4⋊Q811yescharacteristic
142A4#81913yescomplemented
143C3×C4—31no—
144C3×C4—31no—
145C3×C4—43no—
146C3×C4—43no—
147C3×C4C4⋊S411yescharacteristic
148C3×C4C2×SL(2,ℤ/4)11yescharacteristic
149C32—41noSylow
150C23—21no—
151C23—31no—
152C23—31no—
153C23—61no—
154C23C4⋊(C3⋊Dic3)11yescharacteristic
155C2×C4—31no—
156C2×C4—31no—
157C2×C4—31no—
158C2×C4—31no—
159C2×C4—31no—
160C2×C4—31no—
161C2×C4—31no—
162C2×C4—61no—
163C2×C4C2×C3⋊S411yescharacteristic
164C8—32no—
165C8—362no—
166C8—362no—
167C8C3⋊SL(2,ℤ/4)12yes—
168C2×C3—21no—
169C2×C3—31no—
170C2×C3—31no—
171C2×C3—43no—
172C2×C3—61no—
173C2×C3—83no—
174C2×C3C4⋊SL(2,ℤ/4)11yescharacteristic
175C22—31no—
176C22—31no—
177C22—32no—
178C22—31no—
179C22—61no—
180C22—61no—
181C22—61no—
182C22#6364611yescharacteristic, complemented
183C22#6425911yescharacteristic
184C4—31no—
185C4—31no—
186C4C4⋊(C3⋊S4)11yescharacteristic
187C4C2×C3⋊SL(2,ℤ/4)11yescharacteristic
188C3—43no—
189C3#7310511yescharacteristic, complemented
190C2—21no—
191C2—31no—
192C2—31no—
193C2—61no—
194C2C4⋊(C3⋊SL(2,ℤ/4))11yescharacteristic
subgroupG/H
centerC4C4⋊(C3⋊S4)
commutatorC3×C4×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC23×C3×C8D3
socleC23×C3C4⋊Dic3
prime radicalC22×C3×A4Q8
cosocleC2×C3×C4×A4C22
hypercenterC2×C8C3⋊S4
hypocenterC3×A4#108
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
73. C3×A4#108semidirect
140. C22×C3#819semidirect
142. A4#819semidirect
182. C22#63646semidirect
189. C3#73105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
#105936432
#731053
#719773
#636464