Finite Group Databasebeta

← #11782822

Subgroups — #11782822

Order 1152.

558 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 141 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×#487C211yesmaximal, characteristic, complemented
2#10592792C211yesmaximal, characteristic, complemented
3#10592787C211yesmaximal, characteristic
4#10592784C211yesmaximal, characteristic
5#10592777C211yesmaximal, characteristic, complemented
6#10592393C211yesmaximal, characteristic
7#10589321C211yesmaximal, characteristic, complemented
8#71224—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3755—22no—
12#64083C2211yescharacteristic
13#64078C2211yescharacteristic
14C32×#103—22no—
15C32×C4×C8C2211yescharacteristic
16#63648—22no—
17#63637—22no—
18#63636—22no—
19#63634—22no—
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#487D314yescomplemented
23#5093—34no—
24#5088—34no—
25#5085—34no—
26#5078—34no—
27#4694—34no—
28#4455—34no—
29C2×C32×Q8—21no—
30C2×C32×Q8—21no—
31C2×C4⋊(C3⋊D3)—21no—
32C2×C4⋊(C3⋊D3)—21no—
33C2×C4⋊(C3⋊D3)—21no—
34C2×#634—21no—
35C2×C32×C8D412yes—
36C32×C4⋊C4—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C42C2311yescharacteristic
41#3755—44no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C2×C3⋊(C3⋊C8)D412yes—
45C2×C3⋊(C3⋊C8)D412yes—
46#1719—91noSylow
47C3×C4⋊Q8C2×D314yes—
48C3×C4⋊Q8C2×D314yes—
49C2×#215—68no—
50#874—34no—
51#869—34no—
52C3×#103—28no—
53C3×C4×C8C2×D314yes—
54#821—68no—
55#810—68no—
56#809—68no—
57#807—68no—
58C4×C3⋊C8—34no—
59C4×C3⋊C8—34no—
60C22×C3⋊D3—41no—
61C32×Q8—42no—
62C32×Q8—42no—
63C2×C32×C4—41no—
64C2×C32×C4—41no—
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C3⋊Dic3—41no—
69C4⋊(C3⋊D3)—42no—
70C4⋊(C3⋊D3)—42no—
71C4⋊(C3⋊D3)—42no—
72#634—42no—
73C32×C8—22no—
74C3⋊(C3⋊C8)—22no—
75C3⋊(C3⋊C8)—22no—
76#500—91no—
77#492—91no—
78#487—91no—
79#487C3⋊D311yescharacteristic, complemented
80#486—91no—
81#486—91no—
82#322—91no—
83C2×C3×Q8—24no—
84C2×C3×Q8—24no—
85C2×D12—64no—
86C2×D12—64no—
87C2×D12—64no—
88C2×Dic6—64no—
89C2×C3×C8#6718yes—
90C3×C4⋊C4—24no—
91C3×C4⋊C4—24no—
92C3×C4⋊C4—24no—
93C3×C4⋊C4—24no—
94C3×C42C22×D314yes—
95#215—1216no—
96C4⋊Dic3—64no—
97C4⋊Dic3—64no—
98C2×C3⋊C8—38no—
99C2×C3⋊C8—38no—
100C22×C32#12711yescharacteristic
101C2×C3⋊D3—81no—
102C2×C3⋊D3—81no—
103C2×C3⋊D3—81no—
104C32×C4—81no—
105C32×C4—81no—
106C32×C4#13512yes—
107C32×C4AGL(1,ℤ/8)12yes—
108C32×C4#13712yes—
109C3⋊Dic3—81no—
110C2×SD16—182no—
111C4⋊Q8—91no—
112C4⋊Q8C2×C3⋊D311yescharacteristic
113C4⋊Q8C2×C3⋊D311yescharacteristic
114#127—91no—
115#107—182no—
116#103—22no—
117#103—182no—
118#102—182no—
119#102—182no—
120C4×C8—91no—
121C4×C8—91no—
122C4×C8C2×C3⋊D311yescharacteristic
123C22×D3—124no—
124C3×Q8—48no—
125C3×Q8—48no—
126C2×C3×C4—44no—
127C2×C3×C4—44no—
128C2×C3×C4D3×D414yes—
129C2×C3×C4D3×D414yes—
130C2×C3×C4C2×#6714yes—
131C2×Dic3—124no—
132D12—128no—
133D12—128no—
134D12—128no—
135Dic6—128no—
136C3×C8—28no—
137C3⋊C8—68no—
138C3⋊C8—68no—
139C2×C32#49511yescharacteristic
140C2×C32#49611yescharacteristic
141C2×C32#49711yescharacteristic
142C3⋊D3—161no—
143C2×Q8—21no—
144C2×Q8—21no—
145C2×Q8—181no—
146C2×D4—181no—
147C2×D4—181no—
148C2×D4—181no—
149SD16—364no—
150C2×C8—92no—
151C2×C8—92no—
152C2×C8#63812yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—181no—
158C4⋊C4—181no—
159C42C22×C3⋊D311yescharacteristic
160C22×C3#94014yes—
161C2×D3—244no—
162C2×D3—244no—
163C2×D3—244no—
164C3×C4—84no—
165C3×C4—84no—
166C3×C4#91418yes—
167C3×C4#91818yes—
168C3×C4#95018yes—
169Dic3—244no—
170C32#171911yescharacteristic, complemented, Sylow
171C23—361no—
172Q8—42no—
173Q8—42no—
174Q8—362no—
175D4—362no—
176D4—362no—
177D4—362no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—361no—
181C2×C4D4×C3⋊D311yescharacteristic
182C2×C4D4×C3⋊D311yescharacteristic
183C2×C4C2×#63811yescharacteristic
184C8—22no—
185C8—182no—
186C8—182no—
187C2×C3#505914yes—
188C2×C3#517614yes—
189C2×C3#519014yes—
190D3—484no—
191C22—721no—
192C22—721no—
193C22—721no—
194C22#6414911yescharacteristic
195C4—81no—
196C4—81no—
197C4—721no—
198C4#6412312yes—
199C4#6412712yes—
200C4#6415912yes—
201C3#7122414yescomplemented
202C2—1441no—
203C2#1059275811yescharacteristic
204C2#1059287511yescharacteristic
205C2#1059288911yescharacteristic
subgroupG/H
centerC22#64149
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#487C2
socleC22×C32#127
prime radical#64083C22
hypercenter#487C3⋊D3
hypocenterC32#1719
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. C32×#487C2semidirect
2. #10592792C2semidirect
5. #10592777C2semidirect
7. #10589321C2semidirect
22. C3×#487D3semidirect
79. #487C3⋊D3semidirect
170. C32#1719semidirect
201. C3#71224semidirect

Maximal subgroups

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

subgroupindex
C32×#4872
#105927922
#105927872
#105927842
#105927772
#105923932
#105893212
#712243