Finite Group Databasebeta

← #11782574

Subgroups — #11782574

Order 1152.

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

normal subgroups only

This group has 534 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#10592787C211yesmaximal, characteristic
5#10592778C211yesmaximal, characteristic, complemented
6#10592393C211yesmaximal, characteristic
7C8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#71215—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11#64083C2211yescharacteristic
12#64078C2211yescharacteristic
13C32×#103—22no—
14C32×C4×C8C2211yescharacteristic
15#63662—22no—
16#63648—22no—
17#63637—22no—
18#63636—22no—
19#63636—22no—
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#487D314yescomplemented
23#5093—34no—
24#5088—34no—
25#5088—34no—
26#5079—34no—
27#4694—34no—
28C8×C3⋊C8—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
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)—21no—
43C2×C3⋊(C3⋊C8)D412yes—
44C2×C3⋊(C3⋊C8)D412yes—
45#1711—91noSylow
46C3×C4⋊Q8C2×D314yes—
47C3×C4⋊Q8C2×D314yes—
48#874—34no—
49#869—34no—
50C3×#103—28no—
51C3×C4×C8C2×D314yes—
52#835—68no—
53#821—68no—
54#810—68no—
55#809—68no—
56#809—68no—
57C4×C3⋊C8—34no—
58C4×C3⋊C8—34no—
59C22×C3⋊D3—41no—
60C32×Q8—42no—
61C32×Q8—42no—
62C2×C32×C4—41no—
63C2×C32×C4—41no—
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3—41no—
68C4⋊(C3⋊D3)—42no—
69C4⋊(C3⋊D3)—42no—
70C4⋊(C3⋊D3)—42no—
71#634—42no—
72C32×C8—22no—
73C3⋊(C3⋊C8)—22no—
74C3⋊(C3⋊C8)—22no—
75#487—91no—
76#487—91no—
77#487C3⋊D311yescharacteristic, complemented
78#486—91no—
79#486—91no—
80#486—91no—
81C82—91no—
82C2×C3×Q8—24no—
83C2×C3×Q8—24no—
84C2×D12—64no—
85C2×D12—64no—
86C2×D12—64no—
87C2×Dic6—64no—
88C2×C3×C8#6718yes—
89C3×C4⋊C4—24no—
90C3×C4⋊C4—24no—
91C3×C4⋊C4—24no—
92C3×C4⋊C4—24no—
93C3×C42C22×D314yes—
94C4⋊Dic3—64no—
95C4⋊Dic3—64no—
96C2×C3⋊C8—38no—
97C2×C3⋊C8—38no—
98C22×C32#12711yescharacteristic
99C2×C3⋊D3—81no—
100C2×C3⋊D3—81no—
101C2×C3⋊D3—81no—
102C32×C4—81no—
103C32×C4—81no—
104C32×C4#13512yes—
105C32×C4#13512yes—
106C32×C4#13512yes—
107C3⋊Dic3—81no—
108C4⋊Q8—91no—
109C4⋊Q8C2×C3⋊D311yescharacteristic
110C4⋊Q8C2×C3⋊D311yescharacteristic
111#127—91no—
112#103—22no—
113#103—182no—
114#103—182no—
115#102—182no—
116#102—182no—
117#102—182no—
118C4×C8—91no—
119C4×C8—91no—
120C4×C8C2×C3⋊D311yescharacteristic
121C22×D3—124no—
122C3×Q8—48no—
123C3×Q8—48no—
124C2×C3×C4—44no—
125C2×C3×C4—44no—
126C2×C3×C4D3×D414yes—
127C2×C3×C4D3×D414yes—
128C2×C3×C4C2×#6714yes—
129C2×Dic3—124no—
130D12—128no—
131D12—128no—
132D12—128no—
133Dic6—128no—
134C3×C8—28no—
135C3⋊C8—68no—
136C3⋊C8—68no—
137C2×C32#49511yescharacteristic
138C2×C32#49511yescharacteristic
139C2×C32#49511yescharacteristic
140C3⋊D3—161no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—181no—
144C2×D4—181no—
145C2×D4—181no—
146C2×D4—181no—
147C2×C8—92no—
148C2×C8—92no—
149C2×C8#63812yes—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—181no—
155C4⋊C4—181no—
156C42C22×C3⋊D311yescharacteristic
157C22×C3#94014yes—
158C2×D3—244no—
159C2×D3—244no—
160C2×D3—244no—
161C3×C4—84no—
162C3×C4—84no—
163C3×C4#91618yes—
164C3×C4#91918yes—
165C3×C4#95018yes—
166Dic3—244no—
167C32#171111yescharacteristic, complemented, Sylow
168C23—361no—
169Q8—42no—
170Q8—42no—
171Q8—362no—
172D4—362no—
173D4—362no—
174D4—362no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—361no—
178C2×C4D4×C3⋊D311yescharacteristic
179C2×C4D4×C3⋊D311yescharacteristic
180C2×C4C2×#63811yescharacteristic
181C8—22no—
182C8—182no—
183C8—182no—
184C2×C3#505914yes—
185C2×C3#516814yes—
186C2×C3#519114yes—
187D3—484no—
188C22—721no—
189C22—721no—
190C22—721no—
191C22#6414911yescharacteristic
192C4—81no—
193C4—81no—
194C4—721no—
195C4#6412512yes—
196C4#6412812yes—
197C4#6415912yes—
198C3#7121514yescomplemented
199C2—1441no—
200C2#1059275811yescharacteristic
201C2#1059286711yescharacteristic
202C2#1059289011yescharacteristic
subgroupG/H
centerC22#64149
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#487C2
socleC22×C32#127
prime radical#64083C22
hypercenter#487C3⋊D3
hypocenterC32#1711
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. #10592778C2semidirect
7. C8×C3⋊(C3⋊C8)C2semidirect
22. C3×#487D3semidirect
77. #487C3⋊D3semidirect
167. C32#1711semidirect
198. C3#71215semidirect

Maximal subgroups

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

subgroupindex
C32×#4872
#105927922
#105927872
#105927782
#105923932
C8×C3⋊(C3⋊C8)2
#712153