Finite Group Databasebeta

← #11921045

Subgroups — #11921045

Order 1152.

276 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 45 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⋊(#41⋊C3)C211yesmaximal, characteristic
2C4⋊(C3⋊#226)C211yesmaximal, characteristic, complemented
3C3⋊(SL(2,𝔽3)⋊C8)C211yesmaximal, characteristic, complemented
4#73089—33nomaximal
5#71920—31nomaximal
6C2×C3×#41⋊C3—21no—
7C2×C3⋊#226—21no—
8C3×C4×SL(2,𝔽3)C2211yescharacteristic
9#63634—41nomaximal
10C3×#550D311yescharacteristic
11C4⋊(#41⋊C3)D313yes—
12C4⋊#226—33no—
13#5070—31no—
14#5031—31no—
15#5007—31no—
16SL(2,𝔽3)⋊C8—33no—
17#4544—31no—
18#4535—31no—
19D4⋊(C3⋊C8)—31no—
20C3×#41⋊C3—41no—
21C2×C3×SL(2,𝔽3)D411yescharacteristic
22C3⋊#226—41no—
23C32×C4⋊C4—41no—
24C4⋊(C3⋊Dic3)—41no—
25C2×C3⋊(C3⋊C8)—41no—
26#1641—91noSylow
27C2×C3×#41—21no—
28C2×#41⋊C3—23no—
29C2×#226—63no—
30C3×#127—31no—
31C3×#121—61no—
32C3×C4×Q8C2×D311yescharacteristic
33C3×C4×D4—31no—
34C2×#216—61no—
35#869—31no—
36C4×SL(2,𝔽3)C2×D313yes—
37#832—61no—
38#832—62no—
39#810—61no—
40#807—61no—
41#807—123no—
42C4⋊(C3⋊C8)—31no—
43C4⋊(C3⋊C8)—31no—
44C4×C3⋊C8—31no—
45C2×C32×C4—41no—
46C2×C32×C4—81no—
47C2×C3⋊Dic3—81no—
48C3×SL(2,𝔽3)D811yescharacteristic
49C3⋊(C3⋊C8)—42no—
50#550C3⋊D311yescharacteristic
51#486—91no—
52#474—91no—
53#462—91no—
54#331—91no—
55Q8⋊C8—91no—
56D4⋊C8—91no—
57C3×#41—41no—
58C3×#41—121no—
59C2×C3×Q8#6711yescharacteristic
60C2×C3×D4—32no—
61C2×C3×D4—31no—
62C2×C3×D4—61no—
63C22×C3×C4—61no—
64C2×Dic6—61no—
65#41⋊C3—43no—
66C2×SL(2,𝔽3)#6713yes—
67#226—123no—
68C3×C4⋊C4—31no—
69C3×C4⋊C4—43no—
70C3×C4⋊C4S411yescharacteristic
71C3×C22⋊C4—61no—
72C3×C42—31no—
73#216—121no—
74#216—121no—
75C4⋊Dic3—61no—
76C4⋊Dic3—61no—
77C4⋊Dic3—123no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—123no—
82C22×C32—41no—
83C32×C4—41no—
84C32×C4—41no—
85C32×C4—161no—
86C3⋊Dic3—161no—
87C2×#41—21no—
88C2×Q16—181no—
89C4⋊Q8—91no—
90#127—31no—
91#121—61no—
92C4×Q8C2×C3⋊D311yescharacteristic
93C4×D4—31no—
94#107—181no—
95C4⋊C8—91no—
96C4⋊C8—91no—
97#103—181no—
98#102—181no—
99#102—182no—
100C4×C8—91no—
101C23×C3—61no—
102C3×Q8—31no—
103C3×Q8#21311yescharacteristic
104C3×D4—61no—
105C3×D4—61no—
106C3×D4—121no—
107C3×D4—121no—
108C3×D4—122no—
109C2×C3×C4—21no—
110C2×C3×C4—31no—
111C2×C3×C4—31no—
112C2×C3×C4—43no—
113C2×C3×C4—83no—
114C2×C3×C4—121no—
115C2×C3×C4—121no—
116C2×C3×C4C2×S411yescharacteristic
117C2×Dic3—121no—
118C2×Dic3—243no—
119Dic6—121no—
120Dic6—121no—
121SL(2,𝔽3)#21313yes—
122C3⋊C8—121no—
123C3⋊C8—126no—
124C3⋊C8—121no—
125C3⋊C8—121no—
126C2×C32—41no—
127C2×C32—41no—
128C2×C32—41no—
129#41—41no—
130#41—121no—
131C2×Q8—181no—
132C2×Q8#63811yescharacteristic
133C2×D4—32no—
134C2×D4—31no—
135C2×D4—61no—
136C22×C4—61no—
137Q16—361no—
138Q16—361no—
139C2×C8—181no—
140C2×C8—181no—
141C2×C8—181no—
142C4⋊C4—31no—
143C4⋊C4—181no—
144C4⋊C4—181no—
145C4⋊C4C3⋊S411yescharacteristic
146C22⋊C4—61no—
147C42—31no—
148C22×C3—43no—
149C22×C3—121no—
150C22×C3—121no—
151C22×C3—121no—
152C22×C3GL(2,ℤ/4)11yescharacteristic
153C3×C4—31no—
154C3×C4—31no—
155C3×C4—41no—
156C3×C4—43no—
157C3×C4—43no—
158C3×C4—61no—
159C3×C4—163no—
160C3×C4#98411yescharacteristic
161C3×C4#98511yescharacteristic
162Dic3—241no—
163Dic3—483no—
164C32—41noSylow
165C23—61no—
166Q8—31no—
167Q8—361no—
168Q8—361no—
169Q8#375311yescharacteristic
170D4—61no—
171D4—61no—
172D4—121no—
173D4—121no—
174D4—122no—
175C2×C4—21no—
176C2×C4—31no—
177C2×C4—31no—
178C2×C4—121no—
179C2×C4—121no—
180C2×C4—361no—
181C2×C4C2×C3⋊S411yescharacteristic
182C8—361no—
183C8—361no—
184C8—361no—
185C2×C3—43no—
186C2×C3—43no—
187C2×C3—43no—
188C2×C3—241no—
189C2×C3#541511yescharacteristic
190C2×C3#542511yescharacteristic
191C2×C3#542811yescharacteristic
192C22—121no—
193C22—121no—
194C22—121no—
195C22#6426911yescharacteristic
196C4—31no—
197C4—31no—
198C4—41no—
199C4—61no—
200C4—721no—
201C4#6426511yescharacteristic
202C4#6426611yescharacteristic
203C3—43no—
204C3#7308911yescharacteristic, complemented
205C2—241no—
206C2#1059364911yescharacteristic
207C2#1059365911yescharacteristic
208C2#1059366211yescharacteristic
subgroupG/H
centerC22#64269
commutator, cosocleC3×C4×SL(2,𝔽3)C22
FrattiniC2×C4C2×C3⋊S4
FittingC3×#550D3
socleC22×C3GL(2,ℤ/4)
prime radicalC3×C4⋊(#41⋊C3)C2
hypercenterC4⋊C4C3⋊S4
hypocenterC3×SL(2,𝔽3)D8
LCSG ▷ C3×C4×SL(2,𝔽3) ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4⋊(C3⋊#226)C2semidirect
3. C3⋊(SL(2,𝔽3)⋊C8)C2semidirect
204. C3#73089semidirect

Maximal subgroups

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

subgroupindex
C3×C4⋊(#41⋊C3)2
C4⋊(C3⋊#226)2
C3⋊(SL(2,𝔽3)⋊C8)2
#730893
#719203
#636344