Finite Group Databasebeta

← #11782518

Subgroups — #11782518

Order 1152.

451 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 451 conjugacy classes of subgroups — too many to draw. Only its 98 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#10592784C211yesmaximal, characteristic
2C3×#5093C212yesmaximal, complemented
3#10590309C211yesmaximal, characteristic, complemented
4#10590281C212yesmaximal
5C3⋊C82C211yesmaximal, characteristic, complemented
6#71213—32nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8C2×#3755—22no—
9#64083C2211yescharacteristic
10C3×#869C2212yes—
11C4×C3⋊(C3⋊C8)C2211yescharacteristic
12C3×#810—24no—
13C3×C4×C3⋊C8C2212yes—
14#63574—22no—
15#63564—24no—
16C3×#487—32no—
17#5093D312yescomplemented
18#5088—32no—
19#5085—32no—
20#5085—61no—
21#5080—32no—
22#4694—32no—
23C8×C3⋊C8—32no—
24C2×C32×Q8—21no—
25C2×C4⋊(C3⋊D3)—21no—
26C2×C4⋊(C3⋊D3)—22no—
27C2×C3×Dic6—22no—
28C32×C4⋊C4—22no—
29C32×C42C2311yescharacteristic
30#3755—44no—
31C2×C3⋊(C3⋊C8)D412yes—
32C3×C4⋊Dic3—22no—
33C3×C4⋊Dic3—22no—
34C2×C3×C3⋊C8D414yes—
35#1708—91noSylow
36C3×C4⋊Q8—21no—
37C3×C4⋊Q8—32no—
38C3×C4⋊Q8C2×D312yes—
39C2×#215—64no—
40C2×#215—64no—
41#874—32no—
42#874—61no—
43#869C2×D312yes—
44C3×#103—64no—
45C3×C4×C8—32no—
46#821—64no—
47#810—24no—
48#809—64no—
49#808—64no—
50C4×C3⋊C8—32no—
51C4×C3⋊C8—61no—
52C4×C3⋊C8C2×D312yes—
53C22×C3⋊D3—41no—
54C32×Q8—42no—
55C2×C32×C4—41no—
56C2×C32×C4C2×D411yescharacteristic
57C2×C32×C4C2×D412yes—
58C4⋊(C3⋊D3)—42no—
59C4⋊(C3⋊D3)—44no—
60C2×C3×Dic3—42no—
61C3×Dic6—44no—
62C3⋊(C3⋊C8)SD1614yes—
63C3×C3⋊C8—24no—
64#498—91no—
65#492—91no—
66#487—32no—
67#486—92no—
68C82—91no—
69C2×C3×Q8—22no—
70C2×C3×Q8—22no—
71C2×C3×Q8—62no—
72C2×D12—62no—
73C2×D12—62no—
74C2×D12—62no—
75C2×D12—62no—
76C2×D12—122no—
77C2×Dic6—22no—
78C2×C3×C8—34no—
79C3×C4⋊C4—22no—
80C3×C4⋊C4—22no—
81C3×C4⋊C4—42no—
82C3×C4⋊C4—62no—
83C3×C4⋊C4—62no—
84C3×C42—21no—
85C3×C42C22×D312yes—
86#215—128no—
87#215—128no—
88C4⋊Dic3—22no—
89C4⋊Dic3—22no—
90C2×C3⋊C8—34no—
91C2×C3⋊C8—62no—
92C2×C3⋊C8#6714yes—
93C22×C32#12711yescharacteristic
94C2×C3⋊D3—81no—
95C2×C3⋊D3—82no—
96C32×C4—81no—
97C32×C4C2×SD1612yes—
98C32×C4#13514yes—
99C3×Dic3—82no—
100C2×SD16—182no—
101C4⋊Q8—32no—
102C4⋊Q8D3211yescharacteristic
103#127—91no—
104#106—182no—
105#103—64no—
106#102—184no—
107C4×C8—32no—
108C4×C8—91no—
109C22×D3—122no—
110C22×D3—122no—
111C3×Q8—44no—
112C3×Q8—44no—
113C3×Q8—124no—
114C2×C3×C4—22no—
115C2×C3×C4—21no—
116C2×C3×C4—42no—
117C2×C3×C4—42no—
118C2×C3×C4—122no—
119C2×C3×C4D3×D412yes—
120C2×C3×C4D3×D412yes—
121C2×C3×C4C2×#6712yes—
122C2×Dic3—42no—
123D12—124no—
124D12—124no—
125D12—124no—
126D12—124no—
127D12—244no—
128Dic6—44no—
129C3×C8—64no—
130C3⋊C8—24no—
131C3⋊C8—38no—
132C3⋊C8—64no—
133C2×C32#49211yescharacteristic
134C2×C32#49512yes—
135C3⋊D3—161no—
136C2×Q8—21no—
137C2×Q8—62no—
138C2×D4—182no—
139C2×D4—181no—
140SD16—364no—
141C2×C8—34no—
142C2×C8—92no—
143C4⋊C4—22no—
144C4⋊C4—62no—
145C4⋊C4—62no—
146C42C2×D3211yescharacteristic
147C22×C3—21no—
148C22×C3#94012yes—
149C2×D3—242no—
150C2×D3—244no—
151C2×D3—242no—
152C2×D3—242no—
153C2×D3—242no—
154C3×C4—22no—
155C3×C4—24no—
156C3×C4—82no—
157C3×C4—82no—
158C3×C4—242no—
159C3×C4D3×SD1614yes—
160C3×C4#91914yes—
161C3×C4#95014yes—
162Dic3—82no—
163C32#170811yescharacteristic, complemented, Sylow
164C23—361no—
165Q8—42no—
166Q8—124no—
167D4—362no—
168D4—364no—
169C2×C4—41no—
170C2×C4—122no—
171C2×C4D3×#6712yes—
172C2×C4#381111yescharacteristic
173C8—64no—
174C8—94no—
175C2×C3—21no—
176C2×C3—22no—
177C2×C3#505912yes—
178C2×C3#517512yes—
179C2×C3#519112yes—
180D3—482no—
181D3—482no—
182C22—721no—
183C22—722no—
184C22#6397911yescharacteristic
185C4—81no—
186C4—242no—
187C4#6393012yes—
188C4#6394914yes—
189C3—21no—
190C3#7121312yescomplemented
191C2—1441no—
192C2#1059149211yescharacteristic
193C2#1059160912yes—
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#127
prime radical#64083C22
hypercenterC4⋊Q8D32
hypocenterC32#1708
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5093C2semidirect
3. #10590309C2semidirect
5. C3⋊C82C2semidirect
17. #5093D3semidirect
163. C32#1708semidirect
190. C3#71213semidirect

Maximal subgroups

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

subgroupindex
#105927842
C3×#50932
#105903092
#105902812
C3⋊C822
#712133