Finite Group Databasebeta

← #11781170

Subgroups — #11781170

Order 1152.

480 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 121 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#10592783C211yesmaximal, characteristic
2#10592777C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic
4#10592533C211yesmaximal, characteristic
5C32×#333C211yesmaximal, characteristic, complemented
6#10589347C211yesmaximal, characteristic, complemented
7#10589345C211yesmaximal, characteristic, complemented
8#68497—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C2×C8×C3⋊D3—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12#64078C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15#63648—21no—
16#63647—21no—
17#63644—21no—
18#63636—21no—
19#63635—21no—
20#63634—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5084—34no—
25#5078—34no—
26#4842—34no—
27#4834—34no—
28C3×#333D314yescomplemented
29#4481—34no—
30#4479—34no—
31C2×C32×Q8—21no—
32C2×C4⋊(C3⋊D3)D411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×#634—21no—
35C2×C32×C8—21no—
36C2×C32×C8—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C42C2311yescharacteristic
40#3752—21no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)D411yescharacteristic
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C8×C3⋊D3—42no—
48#1675—91noSylow
49C3×C4⋊Q8C2×D314yes—
50C2×D3×C8—64no—
51C4×D12—34no—
52#869—34no—
53C3×C4⋊C8C2×D314yes—
54C3×C4⋊C8C2×D314yes—
55#821—64no—
56(C2×D3)⋊C8—64no—
57#817—64no—
58#809—64no—
59#808—64no—
60#807—64no—
61#807—64no—
62C4⋊(C3⋊C8)—34no—
63C4×C3⋊C8—34no—
64C22×C3⋊D3—21no—
65C32×Q8—81no—
66C2×C32×C4—41no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4#4111yescharacteristic
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—41no—
72C4⋊(C3⋊D3)—21no—
73C4⋊(C3⋊D3)Q1612yes—
74C4×C3⋊D3—41no—
75C4×C3⋊D3—41no—
76#634—81no—
77C32×C8—41no—
78C32×C8—41no—
79C3⋊(C3⋊C8)—21no—
80C3⋊(C3⋊C8)—41no—
81C3⋊(C3⋊C8)SD1612yes—
82#500—91no—
83#476—91no—
84#476—91no—
85C8×D4—91no—
86#335—91no—
87#333—91no—
88#333C3⋊D311yescharacteristic, complemented
89C2×C3×Q8—24no—
90C2×D12—34no—
91C2×C4×D3—64no—
92C2×Dic6—64no—
93C2×C3×C8—24no—
94C2×C3×C8—24no—
95C3×C4⋊C4—24no—
96C3×C4⋊C4—24no—
97C3×C42C22×D314yes—
98(C2×D3)⋊C4—64no—
99C4⋊Dic3—34no—
100C4⋊Dic3—64no—
101C4⋊Dic3—64no—
102C2×C3⋊C8—34no—
103C2×C3⋊C8—34no—
104C2×C3⋊C8—64no—
105D3×C8—128no—
106C22×C32#12111yescharacteristic
107C2×C3⋊D3—22no—
108C2×C3⋊D3—41no—
109C2×C3⋊D3—41no—
110C32×C4—21no—
111C32×C4—81no—
112C32×C4C2×SD1611yescharacteristic
113C32×C4C2×Q1611yescharacteristic
114C32×C4#13511yescharacteristic
115C32×C4#13711yescharacteristic
116C3⋊Dic3—41no—
117C3⋊Dic3—81no—
118C22×C8—181no—
119C4⋊Q8—91no—
120C4⋊Q8C2×C3⋊D311yescharacteristic
121C4×D4—91no—
122#107—181no—
123#107—181no—
124#106—181no—
125#106—181no—
126C4⋊C8—91no—
127C4⋊C8C2×C3⋊D311yescharacteristic
128C4⋊C8C2×C3⋊D311yescharacteristic
129#102—181no—
130#102—181no—
131C22⋊C8—181no—
132C4×C8—91no—
133C22×D3—64no—
134C3×Q8—84no—
135C2×C3×C4—44no—
136C2×C3×C4#23514yes—
137C2×C3×C4D3×D414yes—
138C2×C3×C4D3×D414yes—
139C2×Dic3—64no—
140C2×Dic3—124no—
141D12—38no—
142D12—64no—
143C4×D3—124no—
144C4×D3—124no—
145Dic6—244no—
146C3×C8—44no—
147C3×C8—44no—
148C3⋊C8—38no—
149C3⋊C8—64no—
150C3⋊C8—124no—
151C2×C32#46111yescharacteristic
152C2×C32#46711yescharacteristic
153C2×C32#47211yescharacteristic
154C3⋊D3—42no—
155C2×Q8—21no—
156C2×Q8—181no—
157C2×D4—91no—
158C22×C4—181no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—91no—
162C2×C8—91no—
163C2×C8—181no—
164C2×C8—362no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—91no—
168C4⋊C4—181no—
169C4⋊C4—181no—
170C22⋊C4—181no—
171C42C22×C3⋊D311yescharacteristic
172C22×C3#88414yes—
173C2×D3—68no—
174C2×D3—124no—
175C2×D3—124no—
176C3×C4—24no—
177C3×C4—84no—
178C3×C4D3×SD1614yes—
179C3×C4#91614yes—
180C3×C4D3×Q1614yes—
181C3×C4#91814yes—
182Dic3—124no—
183Dic3—244no—
184C32#167511yescharacteristic, complemented, Sylow
185C23—181no—
186Q8—81no—
187Q8—721no—
188D4—92no—
189D4—181no—
190C2×C4—41no—
191C2×C4—181no—
192C2×C4—361no—
193C2×C4—361no—
194C2×C4—361no—
195C2×C4#382811yescharacteristic
196C2×C4D4×C3⋊D311yescharacteristic
197C2×C4D4×C3⋊D311yescharacteristic
198C8—41no—
199C8—41no—
200C8—92no—
201C8—181no—
202C8—361no—
203C2×C3#474914yes—
204C2×C3#481314yes—
205C2×C3#481814yes—
206D3—128no—
207C22—182no—
208C22—361no—
209C22—361no—
210C22#6409311yescharacteristic
211C4—21no—
212C4—81no—
213C4—361no—
214C4—721no—
215C4SD16×C3⋊D311yescharacteristic
216C4#6412511yescharacteristic
217C4Q16×C3⋊D311yescharacteristic
218C4#6412711yescharacteristic
219C3#6849714yescomplemented
220C2—362no—
221C2#1059244811yescharacteristic
222C2#1059251211yescharacteristic
223C2#1059251711yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#333C2
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#333C3⋊D3
hypocenterC32#1675
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #10592777C2semidirect
5. C32×#333C2semidirect
6. #10589347C2semidirect
7. #10589345C2semidirect
28. C3×#333D3semidirect
88. #333C3⋊D3semidirect
184. C32#1675semidirect
219. C3#68497semidirect

Maximal subgroups

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

subgroupindex
#105927832
#105927772
#105925412
#105925332
C32×#3332
#105893472
#105893452
#684973