Finite Group Databasebeta

← #11920710

Subgroups — #11920710

Order 1152.

262 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 43 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
1#5819⋊C3C211yesmaximal, characteristic
2#10593657C211yesmaximal, characteristic
3C2×C3×GU(2,𝔽3)C211yesmaximal, characteristic
4#73129—31nomaximal
5#70375—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3⋊(#131⋊C3)—21no—
8C3⋊GU(2,𝔽3)—21no—
9C3×GU(2,𝔽3)C411yescharacteristic, complemented
10C3×GU(2,𝔽3)C411yescharacteristic, complemented
11#63577—41nomaximal
12#5819D311yescharacteristic
13#568⋊C3—31no—
14#5423—31no—
15#5423—61no—
16C2×GU(2,𝔽3)D311yescharacteristic
17C2×C3×#104—31no—
18#5236—31no—
19#5125—31no—
20#4924—31no—
21#4559—31no—
22#4523—31no—
23C3×#41⋊C3C2×C411yescharacteristic
24C3×#41⋊C3D411yescharacteristic
25C2×C3×SL(2,𝔽3)Q811yescharacteristic
26#3748—41no—
27C3×#208—41no—
28C2×C3×C3⋊C8—41no—
29#1861—91noSylow
30C2×C3×#41C2×D311yescharacteristic
31C2×#41⋊C3—21no—
32C2×#41⋊C3C2×D311yescharacteristic
33C2×C3×M16—31no—
34C2×C3×C42—31no—
35#948—21no—
36#948—61no—
37#926—31no—
38C2×#208—31no—
39C2×#208—31no—
40C2×#208—31no—
41#131⋊C3—61no—
42GU(2,𝔽3)—62no—
43GU(2,𝔽3)—61no—
44GU(2,𝔽3)Dic311yescharacteristic, complemented
45GU(2,𝔽3)Dic311yescharacteristic, complemented
46C3×#104—31no—
47C3×#104—31no—
48C3×#104—31no—
49C3×#104—31no—
50#837—61no—
51#837—61no—
52#822—121no—
53#819—61no—
54#819—61no—
55C4⋊(C3⋊C8)—62no—
56C2×C32×C4—41no—
57C3×SL(2,𝔽3)C4⋊C411yescharacteristic
58C3⋊(C3⋊C8)—81no—
59C3×C3⋊C8—41no—
60C3×C3⋊C8—41no—
61C3×C3⋊C8—81no—
62#568—31no—
63#430—91no—
64#423—91no—
65#421—91no—
66C2×#104—31no—
67#344—91no—
68#339—91no—
69C3×#41—31no—
70C3×#41—31no—
71C3×#41C4×D311yescharacteristic
72C3×#41#6711yescharacteristic
73C2×C3×Q8Dic611yescharacteristic
74C2×C3×D4—31no—
75C22×C3×C4—31no—
76C22×C3×C4—61no—
77#41⋊C3—21no—
78#41⋊C3—21no—
79#41⋊C3D1211yescharacteristic
80#41⋊C3C2×Dic311yescharacteristic
81C2×SL(2,𝔽3)—21no—
82C2×SL(2,𝔽3)Dic611yescharacteristic
83C3×M16—31no—
84C3×M16—31no—
85C3×M16—61no—
86C3×M16—121no—
87C2×C3×C8—61no—
88C3×C42—31no—
89C3×C42—31no—
90C3×C42—61no—
91#217—61no—
92C4⋊Dic3—61no—
93C4×Dic3—61no—
94#208—31no—
95#208—61no—
96#208—61no—
97#208—61no—
98#208—61no—
99#208—121no—
100#208—241no—
101#208S411yescharacteristic
102C2×C3⋊C8—32no—
103C2×C3⋊C8—41no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C22×C32—41no—
107C32×C4—41no—
108C32×C4—41no—
109C2×#41D3211yescharacteristic
110#131—61no—
111#131—181no—
112C2×M16—31no—
113C2×M16—91no—
114C2×M16—91no—
115C2×M16—91no—
116#117—91no—
117C2×C42—31no—
118#108—181no—
119#108—181no—
120C4⋊C8—182no—
121#104—31no—
122#104—31no—
123#104—31no—
124#104—31no—
125#104—181no—
126#104—181no—
127C23×C3—31no—
128C3×Q8—31no—
129C3×Q8Dic3⋊C411yescharacteristic
130C3×D4—31no—
131C3×D4—31no—
132C3×D4—61no—
133C2×C3×C4—31no—
134C2×C3×C4—31no—
135C2×C3×C4—31no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—41no—
139C2×C3×C4—61no—
140C2×C3×C4—61no—
141C2×C3×C4—81no—
142C2×C3×C4—122no—
143C2×C3×C4C2×S411yescharacteristic
144C2×Dic3—121no—
145SL(2,𝔽3)—21no—
146SL(2,𝔽3)C4⋊Dic311yescharacteristic
147C3×C8—61no—
148C3×C8—61no—
149C3×C8—241no—
150C3⋊C8—21no—
151C3⋊C8—41no—
152C3⋊C8—41no—
153C3⋊C8—61no—
154C3⋊C8—121no—
155C3⋊C8—241no—
156C3⋊C8—242no—
157C2×C32—41no—
158C2×C32—81no—
159#41—31no—
160#41—31no—
161#41D3×Dic311yescharacteristic
162#41#62611yescharacteristic
163C2×Q8#62711yescharacteristic
164C2×D4—31no—
165C22×C4—31no—
166C22×C4—61no—
167M16—31no—
168M16—31no—
169M16—31no—
170M16—61no—
171M16—91no—
172M16—181no—
173M16—181no—
174M16—181no—
175M16—181no—
176C2×C8—61no—
177C2×C8—92no—
178C2×C8—181no—
179C2×C8—181no—
180C4⋊C4—181no—
181C22⋊C4—181no—
182C42—31no—
183C42—31no—
184C42—61no—
185C42—181no—
186C22×C3—31no—
187C22×C3—31no—
188C22×C3—41no—
189C22×C3—81no—
190C22×C3—121no—
191C22×C3A4⋊Q811yescharacteristic
192C3×C4—31no—
193C3×C4—31no—
194C3×C4—41no—
195C3×C4—41no—
196C3×C4—62no—
197C3×C4—81no—
198C3×C4—81no—
199C3×C4—121no—
200C3×C4C4×S411yescharacteristic
201C3×C4GL(2,ℤ/4)11yescharacteristic
202Dic3—241no—
203C32—41noSylow
204C23—31no—
205Q8—31no—
206Q8Dic3⋊Dic311yescharacteristic
207D4—31no—
208D4—31no—
209D4—61no—
210C2×C4—31no—
211C2×C4—31no—
212C2×C4—31no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—61no—
216C2×C4—61no—
217C2×C4—122no—
218C2×C4—361no—
219C2×C4D3×S411yescharacteristic
220C8—61no—
221C8—61no—
222C8—61no—
223C8—181no—
224C8—361no—
225C2×C3—21no—
226C2×C3—41no—
227C2×C3—61no—
228C2×C3—61no—
229C2×C3—81no—
230C2×C3—81no—
231C2×C3—161no—
232C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
233C22—31no—
234C22—31no—
235C22—121no—
236C22#6420411yescharacteristic
237C4—31no—
238C4—31no—
239C4—62no—
240C4—121no—
241C4—721no—
242C4Dic3×S411yescharacteristic
243C4#6421011yescharacteristic
244C3—41no—
245C3—81no—
246C3#7312911yescharacteristic, complemented
247C2—21no—
248C2—61no—
249C2—61no—
250C2SL(2,ℤ/4)⋊Dic311yescharacteristic
subgroupG/H
centerC4#64210
commutatorC3×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC2×C3SL(2,ℤ/4)⋊C4
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C4⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
9. C3×GU(2,𝔽3)C4semidirect
10. C3×GU(2,𝔽3)C4semidirect
44. GU(2,𝔽3)Dic3semidirect
45. GU(2,𝔽3)Dic3semidirect
246. C3#73129semidirect

Maximal subgroups

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

subgroupindex
#5819⋊C32
#105936572
C2×C3×GU(2,𝔽3)2
#731293
#703753
#635774