Finite Group Databasebeta

← #11782427

Subgroups — #11782427

Order 1152.

499 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 499 conjugacy classes of subgroups — too many to draw. Only its 114 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×#5080C212yesmaximal, complemented
3#10590373C212yesmaximal
4#10590309C211yesmaximal, characteristic, complemented
5C3⋊C82C211yesmaximal, characteristic, complemented
6#71332—32nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8C2×#3755—22no—
9#64083C2211yescharacteristic
10C3×#869C2212yes—
11C2×#3717—24no—
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#808—24no—
14C3×C4×C3⋊C8C2212yes—
15#63574—22no—
16C3×#498—32no—
17#5085—32no—
18#5085—32no—
19#5085—61no—
20#5080—32no—
21#5080D312yescomplemented
22#4693—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#3717—48no—
36#1705—91noSylow
37C3×C4⋊Q8—21no—
38C3×C4⋊Q8—32no—
39C3×C4⋊Q8C2×D312yes—
40C2×#215—64no—
41C2×#215—64no—
42C2×#215—64no—
43C2×#204—64no—
44#874—32no—
45#874—61no—
46#869C2×D312yes—
47C3×#106—64no—
48C3×C4×C8—32no—
49#808—24no—
50#808—64no—
51C4×C3⋊C8—32no—
52C4×C3⋊C8—61no—
53C4×C3⋊C8C2×D312yes—
54C22×C3⋊D3—41no—
55C32×Q8—42no—
56C2×C32×C4—41no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C32×C4C2×D412yes—
59C4⋊(C3⋊D3)—42no—
60C4⋊(C3⋊D3)—44no—
61C2×C3×Dic3—42no—
62C3×Dic6—44no—
63C3⋊(C3⋊C8)SD1614yescomplemented
64C3×C3⋊C8SD1618yescomplemented
65#498—32no—
66#498—91no—
67#492—92no—
68#492—91no—
69C82—91no—
70C2×C3×Q8—22no—
71C2×C3×Q8—22no—
72C2×C3×Q8—62no—
73C2×D12—62no—
74C2×D12—62no—
75C2×D12—62no—
76C2×D12—62no—
77C2×D12—122no—
78C2×Dic6—22no—
79C2×C3×C8—34no—
80C3×C4⋊C4—22no—
81C3×C4⋊C4—22no—
82C3×C4⋊C4—42no—
83C3×C4⋊C4—62no—
84C3×C4⋊C4—62no—
85C3×C42—21no—
86C3×C42C22×D312yes—
87#215—128no—
88#215—128no—
89#215—128no—
90C4⋊Dic3—22no—
91C4⋊Dic3—22no—
92C2×C3⋊C8—34no—
93C2×C3⋊C8—62no—
94C2×C3⋊C8#6714yes—
95#204—128no—
96C22×C32#12711yescharacteristic
97C2×C3⋊D3—81no—
98C2×C3⋊D3—82no—
99C32×C4—81no—
100C32×C4C2×SD1612yes—
101C32×C4C2×SD1614yes—
102C3×Dic3—82no—
103C2×SD16—184no—
104C2×SD16—182no—
105C4⋊Q8—32no—
106C4⋊Q8D3211yescharacteristic
107#127—91no—
108#106—64no—
109#106—182no—
110C4×C8—32no—
111C4×C8—91no—
112C22×D3—122no—
113C22×D3—122no—
114C3×Q8—44no—
115C3×Q8—44no—
116C3×Q8—124no—
117C2×C3×C4—22no—
118C2×C3×C4—21no—
119C2×C3×C4—42no—
120C2×C3×C4—42no—
121C2×C3×C4—122no—
122C2×C3×C4D3×D412yes—
123C2×C3×C4D3×D412yes—
124C2×C3×C4C2×#6712yes—
125C2×Dic3—42no—
126D12—124no—
127D12—124no—
128D12—124no—
129D12—124no—
130D12—244no—
131Dic6—44no—
132C3×C8—38no—
133C3⋊C8—38no—
134C3⋊C8—64no—
135C3⋊C8#21518yescomplemented
136C2×C32#49211yescharacteristic
137C2×C32#49212yes—
138C3⋊D3—161no—
139C2×Q8—21no—
140C2×Q8—62no—
141C2×D4—182no—
142C2×D4—181no—
143SD16—368no—
144SD16—364no—
145C2×C8—34no—
146C2×C8—92no—
147C4⋊C4—22no—
148C4⋊C4—62no—
149C4⋊C4—62no—
150C42C2×D3211yescharacteristic
151C22×C3—21no—
152C22×C3#94012yes—
153C2×D3—242no—
154C2×D3—244no—
155C2×D3—242no—
156C2×D3—242no—
157C2×D3—242no—
158C3×C4—22no—
159C3×C4—24no—
160C3×C4—82no—
161C3×C4—82no—
162C3×C4—242no—
163C3×C4D3×SD1614yes—
164C3×C4D3×SD1614yes—
165C3×C4C2×#21514yes—
166Dic3—82no—
167C32#170511yescharacteristic, complemented, Sylow
168C23—361no—
169Q8—42no—
170Q8—124no—
171D4—362no—
172D4—364no—
173C2×C4—41no—
174C2×C4—122no—
175C2×C4D3×#6712yes—
176C2×C4#381111yescharacteristic
177C8—38no—
178C8—94no—
179C2×C3—21no—
180C2×C3—22no—
181C2×C3#508512yes—
182C2×C3#517512yes—
183C2×C3#517512yes—
184D3—482no—
185D3—482no—
186C22—721no—
187C22—722no—
188C22#6397911yescharacteristic
189C4—81no—
190C4—242no—
191C4#6393012yes—
192C4D3×#21514yes—
193C3—21no—
194C3#7133212yescomplemented
195C2—1441no—
196C2#1059149211yescharacteristic
197C2#1059161812yes—
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#127
prime radical#64083C22
hypercenterC4⋊Q8D32
hypocenterC32#1705
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×#5080C2semidirect
4. #10590309C2semidirect
5. C3⋊C82C2semidirect
21. #5080D3semidirect
63. C3⋊(C3⋊C8)SD16semidirect
64. C3×C3⋊C8SD16semidirect
135. C3⋊C8#215semidirect
167. C32#1705semidirect
194. C3#71332semidirect

Maximal subgroups

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

subgroupindex
#105927842
C3×#50802
#105903732
#105903092
C3⋊C822
#713323