Finite Group Databasebeta

← #11920936

Subgroups — #11920936

Order 1152.

276 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 33 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×C4×C42⋊C3C211yesmaximal, characteristic
2C3⋊#4623C212yesmaximal
3#72980—33nomaximal
4#69396—31nomaximal
5#64259—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7#5470—31no—
8C3×C43D311yescharacteristic
9#4924—31no—
10C4×C42⋊C3D313yes—
11#4623—36no—
12#4523—32no—
13#4523—32no—
14C3×C4×A4—41no—
15C3⋊SL(2,ℤ/4)—42no—
16C3×C42⋊C3Q811yescharacteristic, complemented
17#1994—91noSylow
18A4⋊Q8—123no—
19C2×C3×C42—31no—
20C2×C3×C42—31no—
21C2×C3×C42C2×D311yescharacteristic
22#926—32no—
23#924—61no—
24#924—61no—
25C2×#208—32no—
26#870—32no—
27#869—31no—
28#869—31no—
29C4×Dic6—61no—
30C4×Dic6—61no—
31C2×C42⋊C3C2×D313yes—
32C4⋊(C3⋊C8)—61no—
33C4⋊(C3⋊C8)—61no—
34C2×C3×A4—41no—
35#634—161no—
36#533—91no—
37#423—91no—
38C43C3⋊D311yescharacteristic
39#339—92no—
40#339—92no—
41C22×C3×C4—31no—
42C22×C3×C4—31no—
43C22×C3×C4S411yescharacteristic
44C2×Dic6—61no—
45C2×Dic6—61no—
46C4×A4—43no—
47SL(2,ℤ/4)—126no—
48C3×C42—31no—
49C3×C42—31no—
50C3×C42—31no—
51C3×C42—31no—
52C3×C42—31no—
53C3×C42—32no—
54C3×C42—61no—
55C3×C42Dic611yescharacteristic, complemented
56#217—62no—
57C4⋊Dic3—32no—
58C4⋊Dic3—32no—
59C4⋊Dic3—61no—
60C4⋊Dic3—61no—
61Dic3⋊C4—62no—
62Dic3⋊C4—62no—
63C4×Dic3—62no—
64#208—62no—
65#208—62no—
66C2×C3⋊C8—62no—
67C42⋊C3Dic613yescomplemented
68C3×A4—41no—
69C32×C4—161no—
70C3⋊Dic3—162no—
71C2×M16—92no—
72C4⋊Q8—91no—
73C4⋊Q8—91no—
74#125—92no—
75C22⋊Q8—181no—
76C22⋊Q8—181no—
77C4×Q8—181no—
78C4×Q8—181no—
79#117—92no—
80C2×C42—31no—
81C2×C42—31no—
82C2×C42C2×C3⋊D311yescharacteristic
83C4⋊C8—181no—
84C4⋊C8—181no—
85C23×C3C2×S411yescharacteristic
86C2×A4—43no—
87C2×C3×C4—31no—
88C2×C3×C4—31no—
89C2×C3×C4—31no—
90C2×C3×C4—31no—
91C2×C3×C4—31no—
92C2×C3×C4—31no—
93C2×C3×C4—31no—
94C2×C3×C4—31no—
95C2×C3×C4—31no—
96C2×C3×C4—31no—
97C2×C3×C4—62no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100Dic6—122no—
101Dic6—121no—
102Dic6—121no—
103Dic6—483no—
104C3⋊C8—122no—
105C2×C32—161no—
106C2×Q8—181no—
107C2×Q8—181no—
108C22×C4—31no—
109C22×C4—31no—
110C22×C4C3⋊S411yescharacteristic
111M16—182no—
112M16—182no—
113C2×C8—182no—
114C4⋊C4—92no—
115C4⋊C4—92no—
116C4⋊C4—182no—
117C4⋊C4—182no—
118C4⋊C4—181no—
119C4⋊C4—181no—
120C22⋊C4—182no—
121C42—31no—
122C42—31no—
123C42—31no—
124C42—31no—
125C42—31no—
126C42—32no—
127C42—61no—
128C42—182no—
129C42#63411yescharacteristic, complemented
130C22×C3—31no—
131C22×C3—31no—
132C22×C3A4⋊Q811yescharacteristic
133A4—43no—
134C3×C4—31no—
135C3×C4—32no—
136C3×C4—31no—
137C3×C4—31no—
138C3×C4—31no—
139C3×C4—31no—
140C3×C4—61no—
141C3×C4—163no—
142C3×C4#85711yescharacteristic
143Dic3—122no—
144Dic3—122no—
145Dic3—486no—
146C32—161noSylow
147C23C2×C3⋊S411yescharacteristic
148Q8—362no—
149Q8—361no—
150Q8—361no—
151C2×C4—31no—
152C2×C4—31no—
153C2×C4—31no—
154C2×C4—31no—
155C2×C4—31no—
156C2×C4—31no—
157C2×C4—31no—
158C2×C4—31no—
159C2×C4—31no—
160C2×C4—31no—
161C2×C4—62no—
162C2×C4—182no—
163C2×C4—182no—
164C8—362no—
165C2×C3—31no—
166C2×C3—31no—
167C2×C3—163no—
168C2×C3C2×#85711yescharacteristic
169C22—31no—
170C22—31no—
171C22#6425911yescharacteristic
172C4—31no—
173C4—31no—
174C4—31no—
175C4—31no—
176C4—32no—
177C4—31no—
178C4—61no—
179C4—362no—
180C4—362no—
181C4C3⋊#85711yescharacteristic
182C3—163no—
183C3#7298011yescharacteristic, complemented
184C2—31no—
185C2—31no—
186C2C2×C3⋊#85711yescharacteristic
subgroupG/H
centerC2C2×C3⋊#857
commutator, prime radical, cosocleC2×C3×C42⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC3×C43D3
socleC23×C3C2×S4
hypercenterC4C3⋊#857
hypocenterC3×C42⋊C3Q8
LCSG ▷ C2×C3×C42⋊C3 ▷ C3×C42⋊C3
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
16. C3×C42⋊C3Q8semidirect
55. C3×C42Dic6semidirect
67. C42⋊C3Dic6semidirect
129. C42#634semidirect
183. C3#72980semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C42⋊C32
C3⋊#46232
#729803
#693963
#642594