Finite Group Databasebeta

← #11920697

Subgroups — #11920697

Order 1152.

277 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 277 conjugacy classes of subgroups — too many to draw. Only its 47 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⋊C3)C211yesmaximal, characteristic
2C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic
3C3×#5424C211yesmaximal, characteristic
4#73122—31nomaximal
5#70292—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3⋊(#131⋊C3)—21no—
8C3⋊GU(2,𝔽3)—21no—
9C3×#859C411yescharacteristic, complemented
10C3×#859C411yescharacteristic, complemented
11Dic3⋊(C3⋊C8)—41nomaximal
12C2×#948D311yescharacteristic
13C2×#131⋊C3—31no—
14#5424D311yescharacteristic
15C2×GU(2,𝔽3)—31no—
16C2×GU(2,𝔽3)—61no—
17C3×#416—31no—
18C2×#837—31no—
19C2×#819—31no—
20#4999—31no—
21#4550—31no—
22#4532—31no—
23C3×#41⋊C3D411yescharacteristic
24C3×#41⋊C3Q811yescharacteristic
25C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
26C2×C3⋊(C3⋊C8)—41no—
27C3×C4×Dic3—41no—
28C2×C3×C3⋊C8—41no—
29#1866—91noSylow
30C2×C3×#41C2×D311yescharacteristic
31C2×#41⋊C3—21no—
32C2×#41⋊C3C2×D311yescharacteristic
33C22×C3×C8—31no—
34C3×#117—31no—
35#948—21no—
36#948—61no—
37C2×C4×Dic3—31no—
38C2×#208—31no—
39C2×#208—31no—
40C22×C3⋊C8—31no—
41#131⋊C3—61no—
42GU(2,𝔽3)—62no—
43GU(2,𝔽3)—61no—
44#859Dic311yescharacteristic, complemented
45#859Dic311yescharacteristic, complemented
46C3×#103—31no—
47C3×#103—31no—
48C3×#102—31no—
49C3×#102—31no—
50#837—61no—
51#837—61no—
52#819—62no—
53Dic3⋊C8—121no—
54C4⋊(C3⋊C8)—61no—
55C4⋊(C3⋊C8)—61no—
56C2×C32×C4—41no—
57C2×C3×Dic3—41no—
58C2×C3×Dic3—41no—
59C3×SL(2,𝔽3)C4⋊C411yescharacteristic
60C3⋊(C3⋊C8)—81no—
61C3×C3⋊C8—81no—
62C2×#131—31no—
63C2×#108—91no—
64#424—91no—
65C2×#104—91no—
66#416—31no—
67#339—91no—
68#336—91no—
69C3×#41—31no—
70C3×#41—31no—
71C3×#41Dic611yescharacteristic
72C3×#41#6711yescharacteristic
73C2×C3×Q8C4×D311yescharacteristic
74C2×C3×D4—31no—
75C22×C3×C4—31no—
76C22×Dic3—61no—
77#41⋊C3—21no—
78#41⋊C3—21no—
79#41⋊C3Dic611yescharacteristic
80#41⋊C3D1211yescharacteristic
81C2×SL(2,𝔽3)—21no—
82C2×SL(2,𝔽3)C2×Dic311yescharacteristic
83C2×C3×C8—31no—
84C2×C3×C8—31no—
85C2×C3×C8—61no—
86C2×C3×C8—61no—
87C2×C3×C8—121no—
88C3×C4⋊C4—31no—
89C3×C4⋊C4—31no—
90C3×C22⋊C4—61no—
91C3×C42—61no—
92C4×Dic3—41no—
93C4×Dic3—61no—
94C4×Dic3—61no—
95#208—32no—
96#208—61no—
97#208—61no—
98#208—61no—
99C2×C3⋊C8—31no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—121no—
104C2×C3⋊C8—241no—
105C2×C3⋊C8S411yescharacteristic
106C22×C32—41no—
107C32×C4—41no—
108C32×C4—41no—
109C3×Dic3—42no—
110C3×Dic3—81no—
111C2×#41D3211yescharacteristic
112#131—61no—
113#131—181no—
114C2×M16—91no—
115C2×M16—91no—
116C22×C8—31no—
117C22×C8—91no—
118#117—31no—
119C2×C42—91no—
120#108—182no—
121C4⋊C8—181no—
122C4⋊C8—181no—
123#104—181no—
124#104—181no—
125#103—31no—
126#103—31no—
127#102—31no—
128#102—31no—
129C23×C3—31no—
130C3×Q8—31no—
131C3×Q8Dic3⋊C411yescharacteristic
132C3×D4—31no—
133C3×D4—31no—
134C3×D4—61no—
135C2×C3×C4—31no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—31no—
140C2×C3×C4—41no—
141C2×C3×C4—61no—
142C2×C3×C4—61no—
143C2×C3×C4—81no—
144C2×C3×C4C2×S411yescharacteristic
145C2×Dic3—41no—
146C2×Dic3—41no—
147C2×Dic3—62no—
148C2×Dic3—121no—
149C2×Dic3—121no—
150SL(2,𝔽3)—21no—
151SL(2,𝔽3)C4⋊Dic311yescharacteristic
152C3×C8—61no—
153C3×C8—61no—
154C3×C8—241no—
155C3⋊C8—21no—
156C3⋊C8—61no—
157C3⋊C8—121no—
158C3⋊C8—241no—
159C3⋊C8—242no—
160C2×C32—41no—
161C2×C32—41no—
162C2×C32—41no—
163#41—31no—
164#41—31no—
165#41#62611yescharacteristic
166#41#62711yescharacteristic
167C2×Q8D3×Dic311yescharacteristic
168C2×D4—31no—
169C22×C4—31no—
170C22×C4—181no—
171M16—92no—
172M16—181no—
173M16—181no—
174M16—181no—
175C2×C8—31no—
176C2×C8—31no—
177C2×C8—31no—
178C2×C8—61no—
179C2×C8—61no—
180C2×C8—91no—
181C2×C8—181no—
182C2×C8—181no—
183C2×C8—181no—
184C4⋊C4—31no—
185C4⋊C4—31no—
186C22⋊C4—61no—
187C42—61no—
188C42—181no—
189C42—181no—
190C22×C3—31no—
191C22×C3—31no—
192C22×C3—41no—
193C22×C3—61no—
194C22×C3—61no—
195C22×C3—81no—
196C22×C3C4×S411yescharacteristic
197C3×C4—31no—
198C3×C4—31no—
199C3×C4—41no—
200C3×C4—41no—
201C3×C4—81no—
202C3×C4—81no—
203C3×C4—121no—
204C3×C4—121no—
205C3×C4A4⋊Q811yescharacteristic
206C3×C4GL(2,ℤ/4)11yescharacteristic
207Dic3—42no—
208Dic3—81no—
209Dic3—122no—
210C32—41noSylow
211C23—31no—
212Q8—31no—
213Q8Dic3⋊Dic311yescharacteristic
214D4—31no—
215D4—31no—
216D4—61no—
217C2×C4—31no—
218C2×C4—31no—
219C2×C4—31no—
220C2×C4—31no—
221C2×C4—31no—
222C2×C4—61no—
223C2×C4—61no—
224C2×C4—182no—
225C2×C4—361no—
226C2×C4—361no—
227C2×C4D3×S411yescharacteristic
228C8—61no—
229C8—61no—
230C8—61no—
231C8—181no—
232C8—361no—
233C2×C3—41no—
234C2×C3—41no—
235C2×C3—41no—
236C2×C3—61no—
237C2×C3—61no—
238C2×C3—81no—
239C2×C3—81no—
240C2×C3—81no—
241C2×C3#540411yescharacteristic
242C2×C3#540511yescharacteristic
243C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
244C22—31no—
245C22—31no—
246C22—61no—
247C22—61no—
248C22Dic3×S411yescharacteristic
249C4—31no—
250C4—31no—
251C4—121no—
252C4—121no—
253C4—362no—
254C4#6420411yescharacteristic
255C4#6421011yescharacteristic
256C3—41no—
257C3—81no—
258C3#7312211yescharacteristic, complemented
259C2—61no—
260C2—61no—
261C2#1059321911yescharacteristic
262C2#1059322111yescharacteristic
263C2SL(2,ℤ/4)⋊Dic311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C4D3×S4
commutatorC2×C3×SL(2,𝔽3)C2×C4
FittingC2×C3×#41C2×D3
socleC22×C3C4×S4
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C4⋊C4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
9. C3×#859C4semidirect
10. C3×#859C4semidirect
44. #859Dic3semidirect
45. #859Dic3semidirect
258. 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⋊C3)2
C2×C3⋊GU(2,𝔽3)2
C3×#54242
#731223
#702923
Dic3⋊(C3⋊C8)4