Finite Group Databasebeta

← #11921078

Subgroups — #11921078

Order 1152.

322 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 59 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×#131⋊C3C211yesmaximal, characteristic
2#10593658C211yesmaximal, characteristic
3C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic
4#73122—33nomaximal
5#72017—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3×#131⋊C3—21no—
8C3⋊GU(2,𝔽3)—21no—
9C3⋊#859C411yescharacteristic, complemented
10C3⋊#859C411yescharacteristic, complemented
11#63641—41nomaximal
12C2×C3×#131D311yescharacteristic
13C2×#131⋊C3D313yes—
14#5424—33no—
15C2×GU(2,𝔽3)—33no—
16C2×#837—31no—
17#5233—31no—
18C2×#822—31no—
19#5102—31no—
20#4555—31no—
21#4550—31no—
22C3×#41⋊C3D411yescharacteristic
23C3×#41⋊C3Q811yescharacteristic
24C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
25C2×C32×C8—41no—
26C4×C3⋊Dic3—41no—
27C2×C3⋊(C3⋊C8)—41no—
28#1866—91noSylow
29C2×C3×#41C2×D311yescharacteristic
30C2×#41⋊C3C2×D313yes—
31C3×#131—21no—
32C3×#131—61no—
33C2×C3×M16—31no—
34C22×C3×C8—31no—
35#926—31no—
36C2×C4×Dic3—31no—
37C2×#208—31no—
38C22×C3⋊C8—31no—
39#131⋊C3—23no—
40GU(2,𝔽3)—63no—
41#859—33no—
42#859—33no—
43#837—61no—
44#837—61no—
45#835—31no—
46#835—31no—
47#832—31no—
48#832—31no—
49#822—62no—
50Dic3⋊C8—61no—
51Dic3⋊C8—61no—
52Dic3⋊C8—123no—
53C2×C32×C4—41no—
54C2×C3⋊Dic3—41no—
55C2×C3⋊Dic3—41no—
56C3×SL(2,𝔽3)C4⋊C411yescharacteristic
57C32×C8—81no—
58C3⋊(C3⋊C8)—81no—
59C2×#131C3⋊D311yescharacteristic
60C2×#108—91no—
61#424—91no—
62C2×#104—91no—
63#416—91no—
64#339—91no—
65#336—91no—
66C3×#41—31no—
67C3×#41—31no—
68C3×#41Dic611yescharacteristic
69C3×#41#6711yescharacteristic
70C2×C3×Q8C4×D311yescharacteristic
71C2×C3×D4—31no—
72C22×C3×C4—31no—
73C22×Dic3—61no—
74#41⋊C3Dic613yes—
75#41⋊C3#6713yes—
76C2×SL(2,𝔽3)C4×D313yes—
77C3×M16—32no—
78C3×M16—61no—
79C2×C3×C8—31no—
80C2×C3×C8—43no—
81C2×C3×C8—61no—
82C2×C3×C8—61no—
83C2×C3×C8S411yescharacteristic
84#217—61no—
85C4⋊Dic3—31no—
86C4⋊Dic3—31no—
87C4×Dic3—61no—
88C4×Dic3—61no—
89C4×Dic3—61no—
90C4×Dic3—123no—
91#208—61no—
92#208—61no—
93C2×C3⋊C8—31no—
94C2×C3⋊C8—31no—
95C2×C3⋊C8—61no—
96C2×C3⋊C8—61no—
97C2×C3⋊C8—61no—
98C2×C3⋊C8—123no—
99C22×C32—41no—
100C32×C4—41no—
101C32×C4—41no—
102C3⋊Dic3—42no—
103C3⋊Dic3—81no—
104C2×#41C2×C3⋊D311yescharacteristic
105#131—21no—
106#131—61no—
107C2×M16—31no—
108C2×M16—91no—
109C22×C8—31no—
110C22×C8—91no—
111#117—91no—
112C2×C42—91no—
113#108—182no—
114C4⋊C8—181no—
115C4⋊C8—181no—
116#104—181no—
117#104—181no—
118#103—91no—
119#103—91no—
120#102—91no—
121#102—91no—
122C23×C3—31no—
123C3×Q8—31no—
124C3×Q8Dic3⋊C411yescharacteristic
125C3×D4—31no—
126C3×D4—31no—
127C3×D4—61no—
128C2×C3×C4—31no—
129C2×C3×C4—31no—
130C2×C3×C4—31no—
131C2×C3×C4—31no—
132C2×C3×C4—31no—
133C2×C3×C4—43no—
134C2×C3×C4C2×S411yescharacteristic
135C2×Dic3—62no—
136C2×Dic3—61no—
137C2×Dic3—61no—
138C2×Dic3—123no—
139C2×Dic3—123no—
140C2×Dic3—121no—
141C2×Dic3—121no—
142SL(2,𝔽3)Dic3⋊C413yes—
143C3×C8—21no—
144C3×C8—61no—
145C3×C8—83no—
146C3⋊C8—61no—
147C3⋊C8—61no—
148C3⋊C8—121no—
149C3⋊C8—243no—
150C2×C32—41no—
151C2×C32—41no—
152C2×C32—41no—
153#41—31no—
154#41—31no—
155#41#63411yescharacteristic
156#41#63811yescharacteristic
157C2×Q8C4×C3⋊D311yescharacteristic
158C2×D4—31no—
159C22×C4—31no—
160C22×C4—181no—
161M16—32no—
162M16—61no—
163M16—181no—
164M16—181no—
165C2×C8—31no—
166C2×C8—61no—
167C2×C8—61no—
168C2×C8—91no—
169C2×C8—91no—
170C2×C8—181no—
171C2×C8—181no—
172C2×C8—181no—
173C2×C8C3⋊S411yescharacteristic
174C4⋊C4—91no—
175C4⋊C4—91no—
176C22⋊C4—181no—
177C42—181no—
178C42—181no—
179C42—181no—
180C22×C3—31no—
181C22×C3—31no—
182C22×C3—43no—
183C22×C3—61no—
184C22×C3—61no—
185C22×C3C4×S411yescharacteristic
186C3×C4—31no—
187C3×C4—31no—
188C3×C4—43no—
189C3×C4—43no—
190C3×C4A4⋊Q811yescharacteristic
191C3×C4GL(2,ℤ/4)11yescharacteristic
192Dic3—126no—
193Dic3—122no—
194Dic3—121no—
195Dic3—121no—
196Dic3—243no—
197C32—41noSylow
198C23—31no—
199Q8—31no—
200Q8#375011yescharacteristic
201D4—31no—
202D4—31no—
203D4—61no—
204C2×C4—31no—
205C2×C4—31no—
206C2×C4—31no—
207C2×C4—31no—
208C2×C4—31no—
209C2×C4—182no—
210C2×C4—181no—
211C2×C4—181no—
212C2×C4—361no—
213C2×C4—361no—
214C2×C4C2×C3⋊S411yescharacteristic
215C8—21no—
216C8—61no—
217C8—181no—
218C8—181no—
219C8—361no—
220C2×C3—43no—
221C2×C3—43no—
222C2×C3—43no—
223C2×C3—61no—
224C2×C3—61no—
225C2×C3#540411yescharacteristic
226C2×C3#540511yescharacteristic
227C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
228C22—31no—
229C22—31no—
230C22—61no—
231C22—61no—
232C22C4×C3⋊S411yescharacteristic
233C4—31no—
234C4—31no—
235C4—362no—
236C4—361no—
237C4—361no—
238C4#6425911yescharacteristic
239C4#6426911yescharacteristic
240C3—43no—
241C3#7312211yescharacteristic, complemented
242C2—61no—
243C2—61no—
244C2#1059363811yescharacteristic
245C2#1059363911yescharacteristic
246C2#1059364511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×C3⋊S4
commutatorC2×C3×SL(2,𝔽3)C2×C4
FittingC2×C3×#131D3
socleC22×C3C4×S4
prime radical, cosocleC2×C3×#41⋊C3C22
hypercenterC2×C8C3⋊S4
hypocenterC3×SL(2,𝔽3)C4⋊C4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
9. C3⋊#859C4semidirect
10. C3⋊#859C4semidirect
241. C3#73122semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#131⋊C32
#105936582
C2×C3⋊GU(2,𝔽3)2
#731223
#720173
#636414