Finite Group Databasebeta

← #11799607

Subgroups — #11799607

Order 1152.

408 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C32×#499C211yesmaximal, characteristic, complemented
2C4×#3745C211yesmaximal, characteristic
3#10589357C211yesmaximal, characteristic
4#10589357C211yesmaximal, characteristic
5#10589356C211yesmaximal, characteristic, complemented
6#10589355C211yesmaximal, characteristic, complemented
7C4⋊(C3⋊(C3⋊C16))C211yesmaximal, characteristic, complemented
8#71356—34nomaximal
9C32×#125—21no—
10C2×#3745C2211yescharacteristic
11C4×C4⋊(C3⋊D3)—21no—
12C32×#107C2211yescharacteristic
13C32×#107C2211yescharacteristic
14C32×#106—21no—
15C32×C4×C8C2211yescharacteristic
16#63648—21no—
17#63645C2211yescharacteristic
18C2×C3⋊(C3⋊C16)C2211yescharacteristic
19C2×C3⋊(C3⋊C16)C2211yescharacteristic
20C3×#499D314yescomplemented
21C4×D24—34no—
22#4491—34no—
23#4491—34no—
24#4490—34no—
25#4489—34no—
26C4⋊(C3⋊C16)—34no—
27C2×C4⋊(C3⋊D3)—21no—
28C2×C4×C3⋊D3—41no—
29C2×C32×C8D411yescharacteristic
30C2×C32×C8C2311yescharacteristic
31C32×C4⋊C4—21no—
32C32×C4⋊C4—21no—
33C32×C4⋊C4—41no—
34C32×C4⋊C4—41no—
35C32×C42D411yescharacteristic
36#3752—41no—
37C4⋊(C3⋊Dic3)—21no—
38#3745—21no—
39#3745Q812yes—
40C3⋊(C3⋊C16)—21no—
41C3⋊(C3⋊C16)—21no—
42#2228—91noSylow
43C3×#125—24no—
44C2×D24—34no—
45C4×D12—64no—
46C3×#107C2×D314yes—
47C3×#107C2×D314yes—
48C3×#106—24no—
49C3×C4×C8C2×D314yes—
50#821—64no—
51#818—34no—
52C2×C3⋊C16—34no—
53C2×C3⋊C16—34no—
54C22×C3⋊D3—41no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4D811yescharacteristic
58C2×C32×C4D811yescharacteristic
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3—41no—
61C4⋊(C3⋊D3)—22no—
62C4⋊(C3⋊D3)—41no—
63C4×C3⋊D3—82no—
64C32×C8—21no—
65C32×C8C2×Q811yescharacteristic
66C32×C8#4111yescharacteristic
67#499C3⋊D311yescharacteristic, complemented
68C4×D8—91no—
69#367—91no—
70#366—91no—
71C4⋊C16—91no—
72#357—91no—
73#357—91no—
74C2×D12—64no—
75C2×C4×D3—124no—
76C2×C3×C8#6714yes—
77C2×C3×C8C22×D314yes—
78C3×C4⋊C4—24no—
79C3×C4⋊C4—24no—
80C3×C4⋊C4—44no—
81C3×C4⋊C4—44no—
82C3×C42#6714yes—
83(C2×D3)⋊C4—124no—
84C4⋊Dic3—64no—
85D24—38no—
86D24—64no—
87C3⋊C16—64no—
88C3⋊C16—64no—
89C22×C32C2×D811yescharacteristic
90C2×C3⋊D3—42no—
91C2×C3⋊D3—81no—
92C2×C3⋊D3—81no—
93C32×C4—21no—
94C32×C4—21no—
95C32×C4—81no—
96C32×C4—81no—
97C32×C4C22⋊Q811yescharacteristic
98C32×C4#13711yescharacteristic
99C3⋊Dic3—81no—
100C2×D8—91no—
101#125—21no—
102C4×D4—181no—
103C2×C16—91no—
104C2×C16—91no—
105#107—91no—
106#107C2×C3⋊D311yescharacteristic
107#107C2×C3⋊D311yescharacteristic
108#106—21no—
109#102—181no—
110C4×C8C2×C3⋊D311yescharacteristic
111C22×D3—124no—
112C2×C3×C4—44no—
113C2×C3×C4—44no—
114C2×C3×C4#21314yes—
115C2×C3×C4#21314yes—
116C2×C3×C4C2×#6714yes—
117C2×Dic3—124no—
118D12—68no—
119D12—124no—
120C4×D3—248no—
121C3×C8—24no—
122C3×C8D3×Q814yes—
123C3×C8#23914yes—
124C2×C32#47411yescharacteristic
125C2×C32#50811yescharacteristic
126C2×C32#50911yescharacteristic
127C3⋊D3—82no—
128C2×D4—181no—
129C22×C4—361no—
130D8—92no—
131D8—181no—
132C2×C8#63811yescharacteristic
133C2×C8C22×C3⋊D311yescharacteristic
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—41no—
137C4⋊C4—41no—
138C4⋊C4—181no—
139C22⋊C4—361no—
140C42#63811yescharacteristic
141C16—181no—
142C16—181no—
143C22×C3C2×#21314yes—
144C2×D3—128no—
145C2×D3—244no—
146C2×D3—244no—
147C3×C4—24no—
148C3×C4—24no—
149C3×C4—84no—
150C3×C4—84no—
151C3×C4#94214yes—
152C3×C4#94614yes—
153Dic3—244no—
154C32#222811yescharacteristic, complemented, Sylow
155C23—361no—
156D4—182no—
157D4—361no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—361no—
161C2×C4—722no—
162C2×C4#375311yescharacteristic
163C2×C4#375311yescharacteristic
164C2×C4C2×#63811yescharacteristic
165C8—21no—
166C8Q8×C3⋊D311yescharacteristic
167C8#383211yescharacteristic
168C2×C3#508714yes—
169C2×C3#519314yes—
170C2×C3#519414yes—
171D3—248no—
172C22—362no—
173C22—721no—
174C22—721no—
175C22C2×#375311yescharacteristic
176C4—21no—
177C4—21no—
178C4—81no—
179C4—81no—
180C4—721no—
181C4#6415111yescharacteristic
182C4#6415511yescharacteristic
183C3#7135614yescomplemented
184C2—722no—
185C2#1059278611yescharacteristic
186C2#1059289211yescharacteristic
187C2#1059289311yescharacteristic
subgroupG/H
centerC22C2×#3753
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#499C2
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenter#499C3⋊D3
hypocenterC32#2228
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
1. C32×#499C2semidirect
5. #10589356C2semidirect
6. #10589355C2semidirect
7. C4⋊(C3⋊(C3⋊C16))C2semidirect
20. C3×#499D3semidirect
67. #499C3⋊D3semidirect
154. C32#2228semidirect
183. C3#71356semidirect

Maximal subgroups

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

subgroupindex
C32×#4992
C4×#37452
#105893572
#105893562
#105893552
C4⋊(C3⋊(C3⋊C16))2
#713563