Finite Group Databasebeta

← #11921046

Subgroups — #11921046

Order 1152.

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

normal subgroups only

This group has 278 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
2#10593625C211yesmaximal, characteristic, complemented
3C3⋊(SL(2,𝔽3)⋊C8)C211yesmaximal, characteristic, complemented
4#73090—33nomaximal
5#71919—31nomaximal
6C2×C3×#41⋊C3—21no—
7C3×C4×SL(2,𝔽3)C2211yescharacteristic
8C3⋊#859—21no—
9#63635—41nomaximal
10C3×#550D311yescharacteristic
11C4⋊(#41⋊C3)D313yes—
12#5391—33no—
13#5076—31no—
14#5021—31no—
15#5008—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
22C32×C4⋊C4—41no—
23C4⋊(C3⋊Dic3)—41no—
24C2×C3⋊(C3⋊C8)—41no—
25#1631—91noSylow
26C2×C3×#41—21no—
27C2×#41⋊C3—23no—
28C3×#127—31no—
29C3×#121—61no—
30C3×C4×Q8C2×D311yescharacteristic
31C3×C4×D4—31no—
32C2×#214—62no—
33#869—31no—
34C4×SL(2,𝔽3)C2×D313yes—
35#859—63no—
36#835—61no—
37#832—61no—
38#808—61no—
39#808—123no—
40#807—61no—
41C4⋊(C3⋊C8)—31no—
42C4⋊(C3⋊C8)—31no—
43C4×C3⋊C8—31no—
44C2×C32×C4—41no—
45C2×C32×C4—81no—
46C2×C3⋊Dic3—81no—
47C3×SL(2,𝔽3)SD1611yescharacteristic, complemented
48C3⋊(C3⋊C8)—42no—
49#550C3⋊D311yescharacteristic
50#492—91no—
51#477—91no—
52#476—91no—
53#331—91no—
54Q8⋊C8—91no—
55D4⋊C8—91no—
56C3×#41—41no—
57C3×#41—121no—
58C2×C3×Q8#6711yescharacteristic
59C2×C3×D4—32no—
60C2×C3×D4—31no—
61C2×C3×D4—61no—
62C22×C3×C4—61no—
63C2×Dic6—61no—
64#41⋊C3—43no—
65C2×SL(2,𝔽3)#6713yes—
66C3×C4⋊C4—31no—
67C3×C4⋊C4—43no—
68C3×C4⋊C4S411yescharacteristic
69C3×C22⋊C4—61no—
70C3×C42—31no—
71#214—124no—
72C4⋊Dic3—61no—
73C4⋊Dic3—61no—
74C4⋊Dic3—123no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8—61no—
77C2×C3⋊C8—61no—
78C2×C3⋊C8—123no—
79C22×C32—41no—
80C32×C4—41no—
81C32×C4—41no—
82C32×C4—161no—
83C3⋊Dic3—161no—
84C2×#41—21no—
85C2×SD16—182no—
86C4⋊Q8—91no—
87#127—31no—
88#121—61no—
89C4×Q8C2×C3⋊D311yescharacteristic
90C4×D4—31no—
91#107—181no—
92#106—181no—
93C4⋊C8—91no—
94C4⋊C8—91no—
95#103—181no—
96#102—181no—
97C4×C8—91no—
98C23×C3—61no—
99C3×Q8—31no—
100C3×Q8#21411yescharacteristic
101C3×D4—61no—
102C3×D4—61no—
103C3×D4—121no—
104C3×D4—121no—
105C3×D4—122no—
106C2×C3×C4—21no—
107C2×C3×C4—31no—
108C2×C3×C4—31no—
109C2×C3×C4—43no—
110C2×C3×C4—83no—
111C2×C3×C4—121no—
112C2×C3×C4—121no—
113C2×C3×C4C2×S411yescharacteristic
114C2×Dic3—121no—
115C2×Dic3—243no—
116Dic6—122no—
117SL(2,𝔽3)#21413yescomplemented
118C3⋊C8—62no—
119C3⋊C8—121no—
120C3⋊C8—126no—
121C3⋊C8—121no—
122C2×C32—41no—
123C2×C32—41no—
124C2×C32—41no—
125#41—41no—
126#41—121no—
127C2×Q8—181no—
128C2×Q8#63811yescharacteristic
129C2×D4—32no—
130C2×D4—31no—
131C2×D4—61no—
132C22×C4—61no—
133SD16—364no—
134C2×C8—181no—
135C2×C8—181no—
136C2×C8—181no—
137C4⋊C4—31no—
138C4⋊C4—181no—
139C4⋊C4—181no—
140C4⋊C4C3⋊S411yescharacteristic
141C22⋊C4—61no—
142C42—31no—
143C22×C3—43no—
144C22×C3—121no—
145C22×C3—121no—
146C22×C3—121no—
147C22×C3GL(2,ℤ/4)11yescharacteristic
148C3×C4—31no—
149C3×C4—31no—
150C3×C4—41no—
151C3×C4—43no—
152C3×C4—43no—
153C3×C4—61no—
154C3×C4—163no—
155C3×C4#98411yescharacteristic
156C3×C4#98511yescharacteristic
157Dic3—241no—
158Dic3—483no—
159C32—41noSylow
160C23—61no—
161Q8—31no—
162Q8—362no—
163Q8#375411yescharacteristic
164D4—61no—
165D4—61no—
166D4—121no—
167D4—121no—
168D4—122no—
169C2×C4—21no—
170C2×C4—31no—
171C2×C4—31no—
172C2×C4—121no—
173C2×C4—121no—
174C2×C4—361no—
175C2×C4C2×C3⋊S411yescharacteristic
176C8—182no—
177C8—361no—
178C8—361no—
179C2×C3—43no—
180C2×C3—43no—
181C2×C3—43no—
182C2×C3—241no—
183C2×C3#541411yescharacteristic
184C2×C3#542511yescharacteristic
185C2×C3#542911yescharacteristic
186C22—121no—
187C22—121no—
188C22—121no—
189C22#6426911yescharacteristic
190C4—31no—
191C4—31no—
192C4—41no—
193C4—61no—
194C4—721no—
195C4#6426511yescharacteristic
196C4#6426611yescharacteristic
197C3—43no—
198C3#7309011yescharacteristic, complemented
199C2—241no—
200C2#1059364811yescharacteristic
201C2#1059365911yescharacteristic
202C2#1059366311yescharacteristic
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)SD16
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. #10593625C2semidirect
3. C3⋊(SL(2,𝔽3)⋊C8)C2semidirect
47. C3×SL(2,𝔽3)SD16semidirect
117. SL(2,𝔽3)#214semidirect
198. C3#73090semidirect

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
#105936252
C3⋊(SL(2,𝔽3)⋊C8)2
#730903
#719193
#636354