Finite Group Databasebeta

← #11799625

Subgroups — #11799625

Order 1152.

408 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 107 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#10592577C211yesmaximal, characteristic, complemented
2#10592571C211yesmaximal, characteristic
3C32×#366C211yesmaximal, characteristic, complemented
4#10589375C211yesmaximal, characteristic
5#10589367C211yesmaximal, characteristic, complemented
6#10589357C211yesmaximal, characteristic
7#10589356C211yesmaximal, characteristic, complemented
8#69334—34nomaximal
9C2×#3745C2211yescharacteristic
10#64102—21no—
11#64099—21no—
12C2×C32×C16C2211yescharacteristic
13C32×#107C2211yescharacteristic
14C32×#107C2211yescharacteristic
15#63645C2211yescharacteristic
16C8×C3⋊Dic3C2211yescharacteristic
17C2×C3⋊(C3⋊C16)C2211yescharacteristic
18#63636—21no—
19#63635—21no—
20#4878—34no—
21#4872—34no—
22C3×#366D314yescomplemented
23#4509—34no—
24Dic3⋊C16—34no—
25#4491—34no—
26#4490—34no—
27C2×C4⋊(C3⋊D3)—21no—
28C2×C4×C3⋊D3—41no—
29C2×C32×C8C2311yescharacteristic
30C32×C4⋊C4—21no—
31C32×C4⋊C4—21no—
32#3752—41no—
33C4⋊(C3⋊Dic3)—21no—
34C4⋊(C3⋊Dic3)—41no—
35#3750—41no—
36C4×C3⋊Dic3D411yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38#3745—21no—
39#3745Q812yes—
40C32×C16—21no—
41C3⋊(C3⋊C16)—21no—
42#2228—91noSylow
43C2×D24—34no—
44#893—64no—
45#890—64no—
46C2×C3×C16C2×D314yes—
47C3×#107C2×D314yes—
48C3×#107C2×D314yes—
49#818—34no—
50C8×Dic3—34no—
51C2×C3⋊C16—34no—
52#809—64no—
53#808—64no—
54C22×C3⋊D3—41no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3D811yescharacteristic
60C2×C3⋊Dic3D811yescharacteristic
61C4⋊(C3⋊D3)—22no—
62C4⋊(C3⋊D3)—41no—
63C4×C3⋊D3—82no—
64C32×C8C2×Q811yescharacteristic
65C32×C8#4111yescharacteristic
66C3⋊(C3⋊C8)—21no—
67#499—91no—
68C4×D8—91no—
69#367—91no—
70#366C3⋊D311yescharacteristic, complemented
71C4⋊C16—91no—
72#357—91no—
73#357—91no—
74C2×D12—64no—
75C2×C4×D3—124no—
76C2×C3×C8C22×D314yes—
77C3×C4⋊C4—24no—
78C3×C4⋊C4—24no—
79(C2×D3)⋊C4—124no—
80C4⋊Dic3—64no—
81C4⋊Dic3—124no—
82Dic3⋊C4—124no—
83C4×Dic3—34no—
84C2×C3⋊C8—34no—
85D24—38no—
86D24—64no—
87C3×C16—24no—
88C3⋊C16—64no—
89C22×C32C2×D811yescharacteristic
90C2×C3⋊D3—42no—
91C2×C3⋊D3—81no—
92C2×C3⋊D3—81no—
93C32×C4—81no—
94C32×C4—81no—
95C32×C4C22⋊Q811yescharacteristic
96C32×C4#13711yescharacteristic
97C3⋊Dic3—21no—
98C3⋊Dic3—21no—
99C3⋊Dic3—81no—
100C2×D8—91no—
101#125—181no—
102C4×D4—181no—
103C2×C16—91no—
104C2×C16C2×C3⋊D311yescharacteristic
105#107—91no—
106#107C2×C3⋊D311yescharacteristic
107#107C2×C3⋊D311yescharacteristic
108#106—181no—
109#102—181no—
110C4×C8—91no—
111C22×D3—124no—
112C2×C3×C4—44no—
113C2×C3×C4—44no—
114C2×C3×C4D3×D414yes—
115C2×Dic3—34no—
116C2×Dic3—34no—
117C2×Dic3—124no—
118D12—68no—
119D12—124no—
120C4×D3—248no—
121C3×C8#23514yes—
122C3×C8D3×Q814yes—
123C3⋊C8—64no—
124C2×C32#47411yescharacteristic
125C2×C32#50811yescharacteristic
126C2×C32#50911yescharacteristic
127C3⋊D3—82no—
128C2×D4—181no—
129C22×C4—361no—
130D8—92no—
131D8—181no—
132C2×C8—91no—
133C2×C8C22×C3⋊D311yescharacteristic
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—181no—
137C4⋊C4—361no—
138C4⋊C4—361no—
139C22⋊C4—361no—
140C42—91no—
141C16—21no—
142C16—181no—
143C22×C3D3×D814yes—
144C2×D3—128no—
145C2×D3—244no—
146C2×D3—244no—
147C3×C4—84no—
148C3×C4—84no—
149C3×C4#89614yes—
150C3×C4#91814yes—
151Dic3—64no—
152Dic3—64no—
153Dic3—244no—
154C32#222811yescharacteristic, complemented, Sylow
155C23—361no—
156D4—182no—
157D4—361no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—361no—
163C2×C4—722no—
164C2×C4D4×C3⋊D311yescharacteristic
165C8—181no—
166C8#382811yescharacteristic
167C8Q8×C3⋊D311yescharacteristic
168C2×C3#489014yes—
169C2×C3#491114yes—
170C2×C3#491914yes—
171D3—248no—
172C22—362no—
173C22—721no—
174C22—721no—
175C22D8×C3⋊D311yescharacteristic
176C4—81no—
177C4—81no—
178C4—181no—
179C4—181no—
180C4—721no—
181C4#6410511yescharacteristic
182C4#6412711yescharacteristic
183C3#6933414yescomplemented
184C2—722no—
185C2#1059258911yescharacteristic
186C2#1059261011yescharacteristic
187C2#1059261811yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#366C2
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenter#366C3⋊D3
hypocenterC32#2228
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
1. #10592577C2semidirect
3. C32×#366C2semidirect
5. #10589367C2semidirect
7. #10589356C2semidirect
22. C3×#366D3semidirect
70. #366C3⋊D3semidirect
154. C32#2228semidirect
183. C3#69334semidirect

Maximal subgroups

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

subgroupindex
#105925772
#105925712
C32×#3662
#105893752
#105893672
#105893572
#105893562
#693343