Finite Group Databasebeta

← #11921070

Subgroups — #11921070

Order 1152.

312 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 61 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×A4×M16C211yesmaximal, characteristic
2#10593643C211yesmaximal, characteristic
3C2×C3⋊(A4⋊C8)C211yesmaximal, characteristic
4#73114—33nomaximal
5#72001—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C3×C8×A4—21no—
8C3⋊(A4⋊C8)—21no—
9C3⋊(A4⋊C8)C412yes—
10#63649—41nomaximal
11C22×C3×M16D311yescharacteristic
12A4×M16D313yes—
13#5409—33no—
14C2×A4⋊C8—33no—
15#5207—31no—
16C2×#830—31no—
17C2×#822—31no—
18C2×#822—31no—
19#4558—31no—
20#4558—31no—
21C22×C3×A4Q811yescharacteristic
22C3×C4×A4C2×C411yescharacteristic
23C3×C4×A4D411yescharacteristic
24C32×M16—41no—
25#3748—41no—
26C2×C3⋊(C3⋊C8)—41no—
27#1855—91noSylow
28C23×C3×C4C2×D311yescharacteristic
29C2×C4×A4C2×D313yes—
30C2×C3×M16—31no—
31C2×C3×M16—31no—
32C2×C3×M16—61no—
33C22×C3×C8—21no—
34C2×#208—31no—
35C2×#208—31no—
36C22×C3⋊C8—31no—
37C22×C3⋊C8—31no—
38C8×A4—23no—
39A4⋊C8—36no—
40A4⋊C8—63no—
41#830—32no—
42#830—32no—
43#830—61no—
44#830—61no—
45#822—62no—
46#822—61no—
47#822—61no—
48#822—123no—
49C2×C3×A4—21no—
50C2×C3×A4C4⋊C411yescharacteristic
51C2×C32×C4—41no—
52C32×C8—81no—
53C3⋊(C3⋊C8)—42no—
54C3⋊(C3⋊C8)—81no—
55C22×M16C3⋊D311yescharacteristic
56C2×#108—91no—
57C2×#108—91no—
58#407—91no—
59C2×C22⋊C8—91no—
60#341—91no—
61#341—91no—
62C24×C3Dic611yescharacteristic
63C22×A4Dic613yes—
64C22×C3×C4—31no—
65C22×C3×C4—31no—
66C22×C3×C4—31no—
67C22×C3×C4—31no—
68C22×C3×C4C4×D311yescharacteristic
69C22×C3×C4#6711yescharacteristic
70C4×A4C4×D313yes—
71C4×A4#6713yes—
72C3×M16—32no—
73C3×M16—31no—
74C3×M16—43no—
75C3×M16—61no—
76C3×M16S411yescharacteristic
77C2×C3×C8—61no—
78C2×C3×C8—61no—
79#208—61no—
80#208—61no—
81#208—61no—
82#208—61no—
83#208—123no—
84C2×C3⋊C8—32no—
85C2×C3⋊C8—32no—
86C2×C3⋊C8—61no—
87C2×C3⋊C8—61no—
88C2×C3⋊C8—61no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—61no—
92C2×C3⋊C8—123no—
93C22×C32—41no—
94C3×A4#10811yescharacteristic, complemented
95C32×C4—41no—
96C32×C4—41no—
97C23×C4C2×C3⋊D311yescharacteristic
98C2×M16—31no—
99C2×M16—31no—
100C2×M16—61no—
101C2×M16—91no—
102C2×M16—91no—
103C22×C8—21no—
104C22×C8—91no—
105C22×C8—91no—
106#108—182no—
107#108—181no—
108#108—181no—
109C22⋊C8—92no—
110C22⋊C8—92no—
111C22⋊C8—181no—
112C22⋊C8—181no—
113C23×C3—21no—
114C23×C3—31no—
115C23×C3—31no—
116C23×C3—61no—
117C23×C3Dic3⋊C411yescharacteristic
118C2×A4—23no—
119C2×A4Dic3⋊C413yes—
120C2×C3×C4—31no—
121C2×C3×C4—31no—
122C2×C3×C4—31no—
123C2×C3×C4—31no—
124C2×C3×C4—31no—
125C2×C3×C4—31no—
126C2×C3×C4—31no—
127C2×C3×C4—43no—
128C2×C3×C4—61no—
129C2×C3×C4C2×S411yescharacteristic
130C3×C8—21no—
131C3×C8—61no—
132C3×C8—83no—
133C3⋊C8—62no—
134C3⋊C8—62no—
135C3⋊C8—126no—
136C3⋊C8—121no—
137C3⋊C8—121no—
138C3⋊C8—243no—
139C2×C32—41no—
140C2×C32—81no—
141C24#63411yescharacteristic
142C22×C4—31no—
143C22×C4—31no—
144C22×C4—31no—
145C22×C4—31no—
146C22×C4C4×C3⋊D311yescharacteristic
147C22×C4#63811yescharacteristic
148M16—32no—
149M16—31no—
150M16—61no—
151M16—181no—
152M16—181no—
153M16—181no—
154M16—181no—
155M16C3⋊S411yescharacteristic
156C2×C8—61no—
157C2×C8—61no—
158C2×C8—92no—
159C2×C8—92no—
160C2×C8—181no—
161C2×C8—181no—
162C2×C8—181no—
163C2×C8—181no—
164C2×C8—181no—
165C2×C8—181no—
166C22×C3—31no—
167C22×C3—31no—
168C22×C3—31no—
169C22×C3—43no—
170C22×C3—61no—
171C22×C3—61no—
172C22×C3—61no—
173C22×C3—61no—
174C22×C3#82211yescharacteristic, complemented
175C22×C3A4⋊Q811yescharacteristic
176A4#82213yescomplemented
177C3×C4—31no—
178C3×C4—31no—
179C3×C4—43no—
180C3×C4—43no—
181C3×C4C4×S411yescharacteristic
182C3×C4GL(2,ℤ/4)11yescharacteristic
183C32—41noSylow
184C23—21no—
185C23—31no—
186C23—31no—
187C23—61no—
188C23#375011yescharacteristic
189C2×C4—31no—
190C2×C4—31no—
191C2×C4—31no—
192C2×C4—31no—
193C2×C4—31no—
194C2×C4—31no—
195C2×C4—31no—
196C2×C4—61no—
197C2×C4C2×C3⋊S411yescharacteristic
198C8—21no—
199C8—61no—
200C8—182no—
201C8—182no—
202C8—361no—
203C8—361no—
204C2×C3—21no—
205C2×C3—31no—
206C2×C3—31no—
207C2×C3—43no—
208C2×C3—61no—
209C2×C3—83no—
210C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
211C22—31no—
212C22—31no—
213C22—31no—
214C22—61no—
215C22—61no—
216C22—61no—
217C22—61no—
218C22#6364911yescharacteristic, complemented
219C22#6425911yescharacteristic
220C4—31no—
221C4—31no—
222C4C4×C3⋊S411yescharacteristic
223C4#6426911yescharacteristic
224C3—43no—
225C3#7311411yescharacteristic, complemented
226C2—21no—
227C2—31no—
228C2—31no—
229C2—61no—
230C2#1059364511yescharacteristic
subgroupG/H
centerC4#64269
commutatorC3×C4×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC22×C3×M16D3
socleC23×C3Dic3⋊C4
prime radicalC22×C3×A4Q8
cosocleC2×C3×C4×A4C22
hypercenterM16C3⋊S4
hypocenterC3×A4#108
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
94. C3×A4#108semidirect
174. C22×C3#822semidirect
176. A4#822semidirect
218. C22#63649semidirect
225. C3#73114semidirect

Maximal subgroups

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

subgroupindex
C3×A4×M162
#105936432
C2×C3⋊(A4⋊C8)2
#731143
#720013
#636494