Finite Group Databasebeta

← #11799985

Subgroups — #11799985

Order 1152.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#10592592C211yesmaximal, characteristic, complemented
2#10592564C211yesmaximal, characteristic
3C32×#365C211yesmaximal, characteristic, complemented
4#10589382C211yesmaximal, characteristic, complemented
5#10589380C211yesmaximal, characteristic, complemented
6#10589361C211yesmaximal, characteristic, complemented
7#10589353C211yesmaximal, characteristic, complemented
8#69313—34nomaximal
9M16×C3⋊D3—21no—
10C2×#3745C2211yescharacteristic
11C2×#3743C2211yescharacteristic
12#64104—21no—
13C32×M32C2211yescharacteristic
14C32×#108C2211yescharacteristic
15C32×#106C2211yescharacteristic
16#63649—21no—
17#63646C2211yescharacteristic
18#63639C2211yescharacteristic
19#63636—21no—
20#4893—34no—
21#4865—34no—
22C3×#365D314yescomplemented
23#4516—34no—
24#4514—34no—
25#4495—34no—
26#4487—34no—
27C2×C4⋊(C3⋊D3)—21no—
28C2×C4⋊(C3⋊D3)—41no—
29C2×C4×C3⋊D3D411yescharacteristic
30C32×M16—21no—
31C2×C32×C8C2311yescharacteristic
32C32×C4⋊C4—21no—
33#3752—41no—
34#3748—21no—
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36#3745—21no—
37#3745—21no—
38#3743—21no—
39#3743—21no—
40#3743—41no—
41C8×C3⋊D3—41no—
42C32×C16—21no—
43C3⋊(C3⋊C16)—21no—
44#2238—91noSylow
45D3×M16—64no—
46C2×D24—34no—
47C2×ΓL(1,𝔽25)—34no—
48#895—64no—
49C3×M32C2×D314yes—
50C3×#108C2×D314yes—
51C3×#106C2×D314yes—
52#822—64no—
53#819—34no—
54#812—34no—
55#809—64no—
56C22×C3⋊D3—41no—
57C22×C3⋊D3SD1611yescharacteristic
58C2×C32×C4—41no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3SD1611yescharacteristic
61C4⋊(C3⋊D3)—41no—
62C4⋊(C3⋊D3)—41no—
63C4⋊(C3⋊D3)—82no—
64C4×C3⋊D3—21no—
65C4×C3⋊D3—21no—
66C32×C8—41no—
67C32×C8#4111yescharacteristic
68C32×C8#4111yescharacteristic
69C3⋊(C3⋊C8)—21no—
70C3⋊(C3⋊C8)—41no—
71#469—91no—
72#430—91no—
73#365—91no—
74#365C3⋊D311yescharacteristic, complemented
75#361—91no—
76#361—91no—
77#349—91no—
78C2×D12—64no—
79C2×D12—124no—
80C2×C4×D3—34no—
81C3×M16—24no—
82C2×C3×C8C22×D314yes—
83C3×C4⋊C4—24no—
84(C2×D3)⋊C4—124no—
85#208—64no—
86C2×C3⋊C8—34no—
87D24—64no—
88D24—64no—
89ΓL(1,𝔽25)—64no—
90ΓL(1,𝔽25)—64no—
91ΓL(1,𝔽25)—124no—
92D3×C8—124no—
93C3×C16—24no—
94C3⋊C16—64no—
95C22×C32C2×SD1611yescharacteristic
96C2×C3⋊D3—21no—
97C2×C3⋊D3—41no—
98C2×C3⋊D3—81no—
99C2×C3⋊D3—81no—
100C2×C3⋊D3—81no—
101C32×C4—81no—
102C32×C4#12311yescharacteristic
103C32×C4AGL(1,ℤ/8)11yescharacteristic
104C3⋊Dic3—21no—
105C2×D8—91no—
106C2×M16—91no—
107C2×M16—181no—
108#121—181no—
109M32—91no—
110M32C2×C3⋊D311yescharacteristic
111#108—91no—
112#108—181no—
113#108C2×C3⋊D311yescharacteristic
114#106C2×C3⋊D311yescharacteristic
115#102—181no—
116C22×D3—34no—
117C22×D3—124no—
118C2×C3×C4—44no—
119C2×C3×C4D3×D414yes—
120C2×Dic3—34no—
121D12—124no—
122D12—124no—
123D12—248no—
124C4×D3—64no—
125C4×D3—64no—
126C3×C8—44no—
127C3×C8#23514yes—
128C3×C8#23914yes—
129C3⋊C8—64no—
130C3⋊C8—124no—
131C2×C32—21no—
132C2×C32#48111yescharacteristic
133C3⋊D3—41no—
134C3⋊D3—161no—
135C2×D4—181no—
136C2×D4—361no—
137C22×C4—91no—
138D8—181no—
139D8—181no—
140M16—21no—
141M16—181no—
142M16—181no—
143M16—181no—
144M16—361no—
145C2×C8—91no—
146C2×C8—361no—
147C2×C8C22×C3⋊D311yescharacteristic
148C4⋊C4—21no—
149C22⋊C4—361no—
150C16—21no—
151C16—181no—
152C22×C3D3×SD1614yes—
153C2×D3—64no—
154C2×D3—124no—
155C2×D3—244no—
156C2×D3—244no—
157C2×D3—244no—
158C3×C4—84no—
159C3×C4#89414yes—
160C3×C4#91414yes—
161Dic3—64no—
162C32#223811yescharacteristic, complemented, Sylow
163C23—91no—
164C23—361no—
165D4—361no—
166D4—361no—
167D4—722no—
168C2×C4—41no—
169C2×C4—91no—
170C2×C4—181no—
171C2×C4—181no—
172C2×C4D4×C3⋊D311yescharacteristic
173C8—41no—
174C8—181no—
175C8—361no—
176C8#382811yescharacteristic
177C8#383211yescharacteristic
178C2×C3—24no—
179C2×C3#486314yes—
180D3—124no—
181D3—484no—
182C22—181no—
183C22—361no—
184C22—721no—
185C22—721no—
186C22—721no—
187C22SD16×C3⋊D311yescharacteristic
188C4—81no—
189C4—181no—
190C4#6410311yescharacteristic
191C4#6412311yescharacteristic
192C3#6931314yescomplemented
193C2—21no—
194C2—361no—
195C2—1441no—
196C2#1059256211yescharacteristic
subgroupG/H
centerC2#10592562
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#365C2
socleC2×C32#481
prime radical#10592564C2
hypercenter#365C3⋊D3
hypocenterC32#2238
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
1. #10592592C2semidirect
3. C32×#365C2semidirect
4. #10589382C2semidirect
5. #10589380C2semidirect
6. #10589361C2semidirect
7. #10589353C2semidirect
22. C3×#365D3semidirect
74. #365C3⋊D3semidirect
162. C32#2238semidirect
192. C3#69313semidirect

Maximal subgroups

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

subgroupindex
#105925922
#105925642
C32×#3652
#105893822
#105893802
#105893612
#105893532
#693133